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  • Random attractors of reaction-diffusion equations without uniqueness driven by nonlinear colored noise
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-16
    Anhui Gu; Bixiang Wang

    This paper is concerned with the asymptotic behavior of solutions of the non-autonomous reaction-diffusion equations driven by nonlinear colored noise defined on unbounded domains. The nonlinear drift and diffusion terms are assumed to be continuous but not necessarily Lipschitz continuous which leads to the non-uniqueness of solutions. We prove the existence and uniqueness of pullback random attractors for the multi-valued non-autonomous cocycles generated by the solution operators. The measurability of the random attractors is established by the method based on the weak upper semicontinuity of the solutions. The asymptotic compactness of the solutions is derived by Ball’s idea of energy equations in order to overcome the non-compactness of Sobolev embeddings on unbounded domains.

    更新日期:2020-01-17
  • Angles in Teichmüller spaces
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-16
    Wen Yang

    We prove that, in any infinite dimensional or asymptotic Teichmüller space, the angles between Teichmüller geodesic rays issuing from a common point, defined by using the law of cosines, do not always exist. As a consequence, any infinite dimensional or asymptotic Teichmüller space equipped with the Teichmüller metric is not a CAT(κ) space for any κ∈R. We also establish a sufficient condition for the angles not to always exist in a Finsler manifold, and apply it to study the Hilbert metrics.

    更新日期:2020-01-17
  • Global hypoellipticity for strongly invariant operators
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-15
    Alexandre Kirilov; Wagner A.A. de Moraes

    In this note, by analyzing the behavior at infinity of the matrix symbol of an invariant operator P with respect to a fixed elliptic operator, we obtain a necessary and sufficient condition to guarantee that P is globally hypoelliptic. As an application, we obtain the characterization of global hypoellipticity on compact Lie groups and examples on the sphere and the torus. We also investigate relations between the global hypoellipticity of P and global subelliptic estimates.

    更新日期:2020-01-15
  • Finite-time blow-up and global boundedness for chemotaxis system with strong logistic dampening
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-14
    Xinyu Tu; Shuyan Qiu

    In the present study, we consider the chemotaxis system with logistic-type superlinear degradation{∂tu1=τ1Δu1−χ1∇⋅(u1∇v)+λ1u1−μ1u1k1,x∈Ω,t>0,∂tu2=τ2Δu2−χ2∇⋅(u2∇v)+λ2u2−μ2u2k2,x∈Ω,t>0,0=Δv−γv+α1u1+α2u2,x∈Ω,t>0, under the homogeneous Neumann boundary condition, where γ>0, τi>0, χi>0, λi∈R, μi>0 , αi>0 (i=1,2). Consider an arbitrary ball Ω=BR(0)⊂Rn,n≥3,R>0, when ki>1(i=1,2), it is shown that for any parameter kˆ=max⁡{k1,k2} satisfieskˆ<{76ifn∈{3,4},1+12(n−1)ifn≥5, there exist nonnegative radially symmetric initial data under suitable conditions such that the corresponding solutions blow up in finite time in the sense thatlim supt↗Tmax(‖u1(⋅,t)‖L∞(Ω)+‖u2(⋅,t)‖L∞(Ω))=∞for some0

    更新日期:2020-01-15
  • Some new upper and lower bounds for the Mills ratio
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-14
    Steven G. From

    In this paper, we present new upper and lower bounds for the Mills ratio of the standard Gaussian law. Several different methods are used to derive these new bounds. One of the methods reproduces the bounds of several different authors in previous works as special cases and is a very general method that produces many new bounds. One of the bounds can be written in terms of hyperbolic sine and inverse hyperbolic sine functions. Some of the bounds involve exponential functions and are improved versions of previously proposed bounds or are improved versions of the new bounds introduced earlier in this paper. Some results from reliability theory and Jensen's inequality are used to improve determinantal inequalities. Some open problems are discussed, and conjectures are made.

    更新日期:2020-01-15
  • Efficient pricing of European options on two underlying assets by frame duality
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-14
    Jing Zhao; Shenghong Li

    The PROJ method for pricing European options on one underlying asset was proposed by J.Lars Kirkby and then was applied to price Bermudan and Asian options. In this paper, we extend the method to higher dimensions, especially two-dimensions in which some exotic options can be priced. Our method does not rely on a-priori truncation of the integration range and exhibits excellent performance compared with other state-of-the-art methods, particularly for fatter-tailed short maturity models. We also discuss the errors introduced in each approximation and give corresponding error bounds. Numerical results on implementation of this method to price for popular two-assets options, under both the geometric Brownian Motion and Variance-Gamma dynamics, demonstrate remarkable accuracy and robustness.

    更新日期:2020-01-15
  • Ground state of the mass-critical inhomogeneous nonlinear Schrödinger functional
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-14
    Thanh Viet Phan

    We study the ground state problem of the nonlinear Schrödinger functional with a mass-critical inhomogeneous nonlinear term. We provide the optimal condition for the existence of ground states and show that in the critical focusing regime there is a universal blow-up profile given by the unique optimizer of a Gagliardo-Nirenberg interpolation inequality.

    更新日期:2020-01-15
  • An extension of Berwald's inequality and its relation to Zhang's inequality
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-14
    David Alonso-Gutiérrez; Julio Bernués; Bernardo González Merino

    In this note prove the following Berwald-type inequality, showing that for any integrable log-concave function f:Rn→[0,∞) and any concave function h:L→[0,∞), where L={(x,t)∈Rn×[0,∞):f(x)≥e−t‖f‖∞}, thenp→(1Γ(1+p)∫Le−tdtdx∫Lhp(x,t)e−tdtdx)1p is decreasing in p∈(−1,∞), extending the range of p where the monotonicity is known to hold true. As an application of this extension, we will provide a new proof of a functional form of Zhang's reverse Petty projection inequality, recently obtained in [3].

    更新日期:2020-01-15
  • Mehler-Heine type formulas for the Krawtchouk polynomials
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-14
    Diego Dominici

    We derive Mehler–Heine type asymptotic expansions for the Krawtchouk polynomials Kn(x;p,N) with n=O(N) and x=o(N). These formulas provide good approximations for Kn(x;p,N) and determine the asymptotic limit of their zeros as n→∞.

    更新日期:2020-01-15
  • L2-regularity of solutions to linear backward stochastic heat equations, and a numerical application
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-14
    Yanqing Wang

    In this work, we mainly explore the L2-regularity for the second component of the solutions to linear backward stochastic heat equations, which is crucial to obtain the convergence of the numerical solutions. As an application, we provide the convergence rate for time-discretized Galerkin approximation of these equations.

    更新日期:2020-01-15
  • On a Ramanujan Type Entire Function and its Zeros
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-13
    Dan Dai; Mourad E.H. Ismail; Xiang-Sheng Wang

    In this paper, we derive some properties of a Ramanujan type entire function. A mild generalization of the Garret-Ismail-Stanton m-version of the Rogers-Ramanujan identities is obtained. Moreover, we investigate the zeros of the Ramanujan type entire function, and our results generalize those for the zeros of the Ramanujan function. Finally, an integral equation related to the Ramanujan type entire function is also derived.

    更新日期:2020-01-13
  • Qualitative analysis on a diffusive predator-prey model with toxins
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-13
    Xiao Yan; Yanling Li; Gaihui Guo

    This paper is concerned with the diffusive predator-prey model with toxins subject to Dirichlet boundary conditions. The uniform persistence of positive solution is given under certain conditions. In addition, by the Liapunov-Schmidt method, the existence and stability of the bifurcation solution from a double eigenvalues are investigated. Moreover, by the fixed point index theory and perturbation theory of eigenvalues, the uniqueness, stability and multiplicity of coexistence states are analyzed when some key parameter changes. Finally, some numerical simulations are presented to verify the theoretical conclusions and further to reflect the importance of parameters to the number of coexistence states.

    更新日期:2020-01-13
  • A remark on the Liouville problem for stationary Navier-Stokes equations in Lorentz and Morrey spaces
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-13
    Oscar Jarrín

    The Liouville problem for the stationary Navier-Stokes equations on the whole space is a challenging open problem who has know several recent contributions. We prove here some Liouville type theorems for these equations provided the velocity field belongs to some Lorentz spaces and then in the more general setting of Morrey spaces. Our theorems correspond to a improvement of some recent results on this problem and contain some well-known results as a particular case.

    更新日期:2020-01-13
  • Singular semilinear elliptic problems with asymptotically linear reaction terms
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-13
    K.S. Vidhya; Lakshmi Sankar

    We consider the problem{−Δu=λK(x)f(u)in B1c,u=0on ∂B1,u(x)→0as |x|→∞, where B1c={x∈Rn||x|>1},n>2, λ is a positive parameter, K belongs to a class of functions which satisfy certain decay assumptions and f belongs to a class of functions which are asymptotically linear and may be singular at the origin. We prove the existence of positive solutions to such problems for certain values of parameter λ. Existence results to similar problems in Rn are also obtained. Our existence results are proved using the Schauder fixed point theorem and the method of sub and super solutions.

    更新日期:2020-01-13
  • Time decay rates of the L3-Norm for strong solutions to the Navier-Stokes equations in R3
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-11
    V.T.T. Duong; D.Q. Khai; N.M. Tri

    Let u∈C([0,∞);L3(R3)) be a strong solution of the Cauchy problem for the 3D Navier-Stokes equations with the initial value u0. We prove that the time decay rates of u in the L3-norm coincide with ones of the heat equation with the initial value |u0|. Our proofs use the theory about the exitstence of local strong solutions, time decay rates of strong solutions when the initial value is small enough, and uniqueness arguments.

    更新日期:2020-01-13
  • Revisiting limit cycles for 3-monomial differential equations
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    Jing Gao; Yulin Zhao

    In the paper [J. Math. Anal. Appl. 428 (2015) 735–749], Gasull et al. study 3-monomial differential equations z˙=Az+Bzkz¯l+Czmz¯n,z∈C. They show that for each p∈N there are differential equations of this type having at least p limit cycles. The proof relies on the study of the subclass of this type having the form z˙=(a+i)z+(b+i)z|z|2(p−2)−5i/2z¯p−1, with a,b∈R,3≤p∈N. In this paper, we revisit the above subclass. We prove that for each 3≤p∈N, there are differential equations of the type of the subclass having at least p+1 limit cycles. Moreover, we give an alternative proof for the main result in the above mentioned paper, and investigate the number and distribution of limit cycles for this subclass of 3-monomial differential equations.

    更新日期:2020-01-11
  • Large deviation for a 2D Cahn-Hilliard-Navier-Stokes model under random influences
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    G. Deugou; T. Tachim Medjo

    In this article, we derive a large deviation principle for a 2D Cahn-Hilliard-Navier-Stokes model under random influences. The model consists of the Navier-Stokes equations for the velocity, coupled with a Cahn-Hilliard equation for the order (phase) parameter. The proof relies on the weak convergence method that was introduced in [3], [4], [5] and based on a variational representation on infinite-dimensional Brownian motion.

    更新日期:2020-01-11
  • A Liouville theorem of Navier-Stokes equations with two periodic variables
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    Xinghong Pan

    In this paper, we study the Liouville theorem of the stationary Navier-Stokes equations in R3. When the solution is periodic in two variables, we can prove that actually the solution is trivial (constant vector) under the assumption that one component of the velocity, vanishing at infinity, has finite Dirichlet integral and the other two components can have some growth with respect to the distance to the origin.

    更新日期:2020-01-11
  • On classical solutions to the Hartree equation
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    Phuong Le

    This paper is concerned with positive classical solutions to the Hartree equation−Δu=(1|x|n−α⁎up)up−1 in Rn. When n≤2, we show that the equation has no positive solution. When n≥3, we prove that the equation has no positive solution if p

    更新日期:2020-01-11
  • Large time behavior of solution to the three-dimensional quantum bipolar drift-diffusion model from semiconductors
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    Fang Liu; Yeping Li

    In this study, we consider the three-dimensional quantum bipolar drift-diffusion model arising from the semiconductor device simulation, which consists of the coupled nonlinear fourth-order parabolic equation and Poisson equation. Based on the results of the self-similar stability for the one-dimensional quantum bipolar drift-diffusion equation, we show the stability of planar self-similar wave for the three-dimensional quantum bipolar drift-diffusion model. Using the energy methods, we present the global existence of smooth solutions for the initial value problem of the three-dimensional quantum bipolar drift-diffusion equation when the initial data are close to the planar self-similar wave. We also show that in large time, the solution of the three-dimensional quantum bipolar drift-diffusion equations tends to the planar self-similar wave, at an algebraic time-decay rate.

    更新日期:2020-01-11
  • Elementary operators on Hilbert modules over prime C⁎-algebras
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    Ljiljana Arambašić; Ilja Gogić

    Let X be a right Hilbert module over a C⁎-algebra A equipped with the canonical operator space structure. We define an elementary operator on X as a map ϕ:X→X for which there exists a finite number of elements ui in the C⁎-algebra B(X) of adjointable operators on X and vi in the multiplier algebra M(A) of A such that ϕ(x)=∑iuixvi for x∈X. If X=A this notion agrees with the standard notion of an elementary operator on A. In this paper we extend Mathieu's theorem for elementary operators on prime C⁎-algebras by showing that the completely bounded norm of each elementary operator on a non-zero Hilbert A-module X agrees with the Haagerup norm of its corresponding tensor in B(X)⊗M(A) if and only if A is a prime C⁎-algebra.

    更新日期:2020-01-11
  • Cauchy problem and vanishing dispersion limit for Schrödinger-improved Boussinesq equations
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    Jishan Fan; Tohru Ozawa

    We study the Cauchy problem and vanishing dispersion limit of the Schrödinger-improved Boussinesq equations in Rn.

    更新日期:2020-01-11
  • Asymptotic behavior in a quasilinear chemotaxis-growth system with indirect signal production
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    Wenji Zhang; Suying Liu; Pengcheng Niu

    We consider a quasilinear chemotaxis system involving logistic source{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+μ(u−uγ),x∈Ω,t>0,vt=Δv−v+w,x∈Ω,t>0,wt=Δw−w+u,x∈Ω,t>0, with nonnegative initial data under homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂Rn(n⩾1). Here, constants μ>0, γ>1, and D, S are smooth functions fulfilling D(s)⩾K0(s+1)α, |S(s)|⩽K1s(s+1)β−1 for all s⩾0 with α,β∈R and K0,K1>0. Then, if β⩽γ−1, the nonnegative classical solution (u,v,w) is global in time and bounded. Moreover, if μ>0 is sufficiently large, this global bounded solution with nonnegative initial data (u0,v0,w0) satisfies‖u(⋅,t)−1‖L∞(Ω)+‖v(⋅,t)−1‖L∞(Ω)+‖w(⋅,t)−1‖L∞(Ω)→0 as t→∞.

    更新日期:2020-01-11
  • Global regularity of the high-dimensional Oldroyd-B model in the corotational case
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    Zhuan Ye

    In this paper, we focus on the global regularity of the high-dimensional incompressible Oldroyd-B model in the corotational case with fractional dissipation (−Δ)αu. More precisely, under the assumption of α≥12+n4, we obtain the global regularity for the corresponding model.

    更新日期:2020-01-11
  • The three-dimensional Gaussian product inequality
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    Guolie Lan; Ze-Chun Hu; Wei Sun

    We prove the 3-dimensional Gaussian product inequality, i.e., for any real-valued centered Gaussian random vector (X,Y,Z) and m∈N, it holds that E[X2mY2mZ2m]≥E[X2m]E[Y2m]E[Z2m]. This settles positively the Gaussian product conjecture in the 3-dimensional case. Our proof is based on some improved inequalities on multi-term products involving 2-dimensional Gaussian random vectors. The improved inequalities are derived using the Gaussian hypergeometric functions and are of independent interest. As by-products, several new combinatorial identities and inequalities are obtained.

    更新日期:2020-01-11
  • Predator-prey interaction systems with non-uniform dispersal in a spatially heterogeneous environment
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    Wonhyung Choi; Inkyung Ahn

    In nature, species typically migrate to regions of favorable habitat that provide sufficient food and conditions beneficial to survival. When resources in a certain region are insufficient, there tends to be high species motility in search of food. Starvation-driven diffusion (SDD), which is affected by the local habitat conditions in heterogeneous environments, is a dispersal strategy that increases species motility when food or another resource is limiting. In this study, to gain an understanding of how nonuniform random dispersal affects the fitness of species in a heterogeneous region, we examine a Lotka-Volterra-type predator-prey model applied to the situation where the movement of predators follows the rules of SDD. The main result of this study is that when a predator diffuses following the rules of SDD and the prey diffuses uniformly, the predator is more likely to invade a region than when it diffuses uniformly. We conclude that dispersal using an SDD strategy increases species fitness from an evolutionary perspective. The results we present are obtained based on an eigenvalue analysis of the semi-trivial solutions for a linearized operator derived from a model with nonuniform random diffusion. Furthermore, the existence and uniqueness property of coexistence state under appropriate conditions are given.

    更新日期:2020-01-11
  • Global Hölder estimates for 2D linearized Monge–Ampère equations with right-hand side in divergence form
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-10
    Nam Q. Le

    We establish global Hölder estimates for solutions to inhomogeneous linearized Monge–Ampère equations in two dimensions with the right hand side being the divergence of a bounded vector field. These equations arise in the semi-geostrophic equations in meteorology and in the approximation of convex functionals subject to a convexity constraint using fourth order Abreu type equations. Our estimates hold under natural assumptions on the domain, boundary data and Monge-Ampère measure being bounded away from zero and infinity. They are an affine invariant and degenerate version of global Hölder estimates by Murthy-Stampacchia and Trudinger for second order elliptic equations in divergence form.

    更新日期:2020-01-11
  • Subshifts, λ-graph bisystems and C⁎-algebras
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-09
    Kengo Matsumoto

    We introduce a notion of λ-graph bisystem that consists of a pair (L−,L+) of two labeled Bratteli diagrams L−,L+ satisfying certain compatibility condition for labeling their edges. It is a two-sided extension of λ-graph system, that has been previously introduced by the author. Its matrix presentation is called a symbolic matrix bisystem. We first show that any λ-graph bisystem presents subshifts and conversely any subshift is presented by a λ-graph bisystem, called the canonical λ-graph bisystem for the subshift. We introduce an algebraically defined relation on symbolic matrix bisystems called properly strong shift equivalence and show that two subshifts are topologically conjugate if and only if their canonical symbolic matrix bisystems are properly strong shift equivalent. A λ-graph bisystem (L−,L+) yields a pair of C⁎-algebras written OL−+,OL+− that are first defined as the C⁎-algebras of certain étale groupoids constructed from (L−,L+). We study structure of the C⁎-algebras, and show that they are universal unital unique C⁎-algebras subject to certain operator relations among canonical generators of partial isometries and projections encoded by the structure of the λ-graph bisystem (L−,L+). If a λ-graph bisystem comes from a λ-graph system of a finite directed graph, then the associated subshift is the two-sided topological Markov shift (ΛA,σA) by its transition matrix A of the graph, and the associated C⁎-algebra OL−+ is isomorphic to the Cuntz–Krieger algebra OA, whereas the other C⁎-algebra OL+− is isomorphic to the crossed product C⁎-algebra C(ΛA)⋊σA⁎Z of the commutative C⁎-algebra C(ΛA) of continuous functions on the shift space ΛA of the two-sided topological Markov shift by the automorphism σA⁎ induced by the homeomorphism of the shift σA. This phenomena shows a duality between Cuntz–Krieger algebra OA and the crossed product C⁎-algebra C(ΛA)⋊σA⁎Z.

    更新日期:2020-01-09
  • The Bohr inequality for holomorphic mappings with lacunary series in several complex variables
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-09
    Xiao-song Liu; Tai-shun Liu

    In this paper, we first give the Bohr inequality of norm type for holomorphic mappings with lacunary series on the unit polydisk in Cn under some restricted conditions. Next we also establish the Bohr inequality of norm type for holomorphic mappings with lacunary series on the unit ball of complex Banach spaces under some additional conditions, and the Bohr inequality of functional type for holomorphic mappings with lacunary series on the unit ball of complex Banach spaces. Our derived results reduce to the corresponding results in one complex variable.

    更新日期:2020-01-09
  • KMS states on the Toeplitz algebras of higher-rank graphs
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-09
    Johannes Christensen

    The Toeplitz algebra TC⁎(Λ) for a finite k-graph Λ is equipped with a continuous one-parameter group αr for each r∈Rk, obtained by composing the map R∋t→(eitr1,…,eitrk)∈Tk with the gauge action on TC⁎(Λ). In this paper we give a complete description of the β-KMS states for the C⁎-dynamical system (TC⁎(Λ),αr) for all finite k-graphs Λ and all values of β∈R and r∈Rk.

    更新日期:2020-01-09
  • Asymptotic analysis of the Dirichlet fractional Laplacian in domains becoming unbounded
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-09
    Vincenzo Ambrosio; Lorenzo Freddi; Roberta Musina

    In this paper we analyze the asymptotic behavior of the Dirichlet fractional Laplacian (−ΔRn+k)s, with s∈(0,1), on bounded domains in Rn+k that become unbounded in the last k-directions. A dimension reduction phenomenon is observed and described via Γ-convergence.

    更新日期:2020-01-09
  • Geometric essence of “compact” operators on Hilbert C⁎-modules
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-09
    Evgenij Troitsky

    We introduce a uniform structure on any Hilbert C⁎-module N and prove the following theorem: suppose, F:M→N is a bounded adjointable morphism of Hilbert C⁎-modules over A and N is countably generated. Then F belongs to the Banach space generated by operators θx,y, θx,y(z):=x〈y,z〉, x∈N, y,z∈M (i.e. F is A-compact, or “compact”) if and only if F maps the unit ball of M to a totally bounded set with respect to this uniform structure (i.e. F is a compact operator in the classical sense).

    更新日期:2020-01-09
  • Convergence analysis of symmetric dual-wind discontinuous Galerkin approximation methods for the obstacle problem
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-08
    Thomas Lewis; Aaron Rapp; Yi Zhang

    This paper formulates and analyzes symmetric dual-wind discontinuous Galerkin (DG) methods for second order elliptic obstacle problem. These new methods follow from the DG differential calculus framework that defines discrete differential operators to replace the continuous differential operators when discretizing a partial differential equation (PDE). We establish optimal a priori error estimates for both linear and quadratic elements provided the exact solution is sufficiently regular. These results are also shown to hold for some non-positive penalty parameters, with the emphasis on zero penalization across all interior and boundary edges. Numerical experiments are provided to validate the theoretical results and gauge the performance of the proposed methods.

    更新日期:2020-01-09
  • Corrigendum to “Characterizations of Morrey type Besov and Triebel-Lizorkin spaces with variable exponents” [J. Math. Anal. Appl. 381 (1) (2011) 280-298]
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-08
    Jingshi Xu

    In this note, we correct a technical error in the proof of Theorem 2.2 in [1].

    更新日期:2020-01-08
  • Real-valued Lipschitz functions and metric properties of functions
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Gerald Beer; M. Isabel Garrido

    The purpose of this article is to explore the very general phenomenon that a function betweeen metric spaces has a particular metric property if and only if whenever it is followed in a composition by an arbitrary real-valued Lipschitz function, the composition has this property. The key tools we use are the Efremovič lemma [21] and a theorem of Garrido and Jaramillo [22] that says that a function h between metric spaces is Lipschitz if and only if whenever it is followed by a Lipschitz real-valued function in a composition, the composition is Lipschitz. We also present a streamlined proof of the Garrido-Jaramillo result itself, but one that still relies on their natural continuous linear operator from the Lipschitz space for the target space to the Lipschitz space for the domain. Separately, we include a highly applicable uniform closure theorem that yields the most important uniform density theorems for Lipschitz-type functions as special cases.

    更新日期:2020-01-07
  • Large deviations for infinite weighted sums of stretched exponential random variables
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Frank Aurzada

    We study the large deviation probabilities of infinite weighted sums of independent random variables that have stretched exponential tails. This generalizes Kiesel and Stadtmüller [12], who study the same objects under the assumption of finite exponential moments, and Gantert et al. [8], who study finite weighted sums with stretched exponential tails.

    更新日期:2020-01-07
  • Discontinuous Galerkin Method for the fully dynamic Biot's Model
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Jing Wen; Yinnian He; Hongbin Chen

    In this paper, a fully discrete scheme of the fully dynamic Biot's model problem is proposed, which is constructed by using interior penalty discontinuous Galerkin method for the spatial approximation and a tailor difference scheme to approximate the first and second order temporal derivative terms. First of all, we prove the existence and uniqueness of solutions of proposed fully discrete scheme in proper norms. Then, based on the error equations a priori error estimates shall be derived for both primal variables displacement and pore pressure. Finally, a series of numerical examples are given to examine the convergence results by using the proposed numerical scheme to solve the fully dynamic Biot's model problem.

    更新日期:2020-01-07
  • Double phase image restoration
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Petteri Harjulehto; Peter Hästö

    In this paper we explore the potential of the double phase functional in an image processing context. To this end, we study minimizers of the double phase energy for functions with bounded variation and show that this energy can be obtained by Γ-convergence or relaxation of regularized functionals. A central tool is a capped fractional maximal function of the derivative of BV functions.

    更新日期:2020-01-07
  • On the integral modulus of continuity of infinitely divisible distributions, especially of stochastic integrals
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    David Berger

    We derive estimates for the integral modulus of continuity of probability densities of infinitely divisible distributions. The paper is splitted into two parts. The first part deals with general infinitely divisible distributions. The second part is concerned with densities of random integrals with respect to a Lévy process. We will see major differences between integrals over compact and non-compact intervals.

    更新日期:2020-01-07
  • Polynomial versions of almost Dunford-Pettis sets and almost limited sets in Banach lattices
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Zhongrui Shi; Yu Wang; Qingying Bu

    Let A be a norm bounded solid subset of a Banach lattice E and n be any positive integer. We prove that A is an almost Dunford-Pettis set if and only if every positive weakly compact n-homogeneous polynomial from E to c0 maps A to a relatively compact set in c0. Moreover, if E is σ-Dedekind complete, we also prove that A is an almost limited set if and only if every positive n-homogeneous polynomial from E to c0 maps A to a relatively compact set in c0.

    更新日期:2020-01-07
  • Tail asymptotics for a state dependent bulk matching queueing system with impatient customers
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Qihui Bu; Yang Song; Liwei Liu

    In this paper, we study a state dependent bulk matching queueing system with impatient customers, where customers and servers visit the system from both sides. Servers provide services in batch with a maximal size and take matching customers away instantly. For characterizing such a queueing system, the corresponding Markov process is constructed by the number of the complete batches of customers and the number of the remaining customers in the incomplete batch. By analyzing this system, we find it difficult to obtain the joint stationary distribution of the Markov process. Therefore, we pay attention to the tail asymptotics for the joint probabilities. Using the matrix analytic method and censoring technique, we obtain the one term and general expansions for the non-zero elements of the rate matrices, where the coefficients of expansions are presented in the closed form. Based on these expansion formulae, the exact tail asymptotic result for the joint stationary probabilities is derived.

    更新日期:2020-01-07
  • Sobolev embeddings in Orlicz and Lorentz spaces with measures
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Andrea Cianchi; Luboš Pick; Lenka Slavíková

    Embedding theorems for Orlicz-Sobolev spaces into Orlicz or Orlicz-Lorentz spaces in domains in Rn, endowed with a Frostman measure, are offered. Parallel embeddings for Lorentz-Sobolev spaces into (generalized) Lorentz spaces are also established. The relevant embeddings yield an optimal target norm, in the relevant classes, whenever it does exist. In particular, various results available in the literature are improved by special choices of the function spaces and of the measure.

    更新日期:2020-01-07
  • Asymptotic properties of standing waves for Maxwell-Schrödinger-Poisson system
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Tingxi Hu; Lu Lu

    In this paper, we study the asymptotic properties of minimizers for a class of constraint minimization problems derived from the Maxwell-Schrödinger-Poisson system−Δu−(|u|2⁎|x|−1)u−α|u|2pu−μpu=0,x∈R3 on the L2-spheres Aλ={u∈H1(R3):∫R3|u|2dx=λ}, where α,p>0. Let λ⁎=‖Q23‖22, and Q23 is the unique (up to translations) positive radial solution of −3p2Δu+2−p2u−|u|2pu=0 in R3 with p=23. We prove that if λ<α−32λ⁎, then minimizers are compact in Aλ as p↗23. On the contraty, if λ>α−32λ⁎, by directly using asymptotic analysis, we prove that all minimizers must blow up and give the detailed asymptotic behavior of minimizers.

    更新日期:2020-01-07
  • Asymptotic stability of planar rarefaction wave to 3D micropolar equations
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Guiqiong Gong; Lan Zhang

    We are concerned with the large-time behavior of the Cauchy problem to the 3d micropolar fluids in an infinite long flat nozzle domain R×T2. In one dimensional case, this system tends time-asymptotically to the Navier–Stokes equations. That is to say, the basic wave patterns to the compressible micropolar fluids model are stable. Hence, in this paper we consider the nonlinear stability of planar rarefaction wave to the corresponding three dimensional model. Some cancellations on the flux terms and viscous terms are crucial. Moreover, a proper combining of damping term and rotation terms can provide an extra regularity of w.

    更新日期:2020-01-07
  • A maximal energy pointset configuration problem
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Braxton Osting; Brian Simanek

    We consider the extremal pointset configuration problem of maximizing a kernel-based energy subject to the geometric constraints that the points are contained in a fixed set, the pairwise distances are bounded below, and that every closed ball of fixed radius contains at least one point. We also formulate an extremal density problem, whose solution provides an upper bound for the pointset configuration problem in the limit as the number of points tends to infinity. Existence of solutions to both problems is established and the relationship between the parameters in the two problems is studied. Several examples are studied in detail, including the density problem for the d-dimensional ball and sphere, where the solution can be computed exactly using rearrangement inequalities. We develop a computational method for the density problem that is very similar to the Merriman-Bence-Osher (MBO) diffusion-generated method. The method is proven to be increasing for all non-stationary iterations and is applied to study more examples.

    更新日期:2020-01-07
  • Dynamical behavior of non-autonomous fractional stochastic reaction-diffusion equations
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Qianqian Bai; Ji Shu; Linyan Li; Hui Li

    In this paper, we investigate the asymptotic behavior of solutions for the non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with s∈(0,1). We prove the existence and uniqueness of tempered pullback random attractors for the equations in a bounded domain U by the compactness of Sobolev embedding Hs(U)↪L2(U), which is different from the previous work (B. Wang, Asymptotic behavior of non-autonomous fractional stochastic reaction-diffusion equations, Nonlinear Analysis, 158(2017)60-82).

    更新日期:2020-01-07
  • Regularity of quasi-minimizers for non-uniformly elliptic integrals
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-07
    Stefano Biagi; Giovanni Cupini; Elvira Mascolo

    In this paper we consider a class of non-uniformly elliptic integral functionals and we prove the local boundedness of the quasi-minimizers. Our approach is based on a suitable adaptation of the celebrated De Giorgi proof, and it relies on an appropriate Caccioppoli-type inequality.

    更新日期:2020-01-07
  • Complete bifurcation diagram and global phase portraits of Liénard differential equations of degree four
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2019-12-27
    Xiaofeng Chen; Hebai Chen

    Li and Llibre in [J. Differential Equations 252 (2012) 3142–3162] proved that a Liénard system of degree four: dxdt=y−(ax+bx2+cx3+x4), dydt=−x has at most one limit cycle. Moreover, the limit cycle is stable and hyperbolic if it exists. Based on their works, the aim of this paper is to give the complete bifurcation diagram and global phase portraits in the Poincaré disc of this system further. First we analyze the equilibria at both finity and infinity. Then, a necessary and sufficient condition for existence of separatrix loop is founded by the rotation property. Moreover, a necessary and sufficient condition of the existence of limit cycles is also obtained. Finally, we show that the complete bifurcation diagram includes one Hopf bifurcation surface and one bifurcation surface of separatrix loop.

    更新日期:2020-01-04
  • Variational inequality with almost history-dependent operator for frictionless contact problems
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2019-12-30
    Stanisław Migórski; Dariusz Pączka

    We study two quasistatic contact problems which describe the frictionless contact between a body and deformable foundation on an infinite time interval. The contact is modelled by the normal compliance condition with limited penetration and memory. The first problem deals with evolution of a body made of a viscoplastic material and in the second problem the material is viscoelastic with long memory. The constitutive functions of these materials have a non-polynomial growth. For each problem we derive a variational formulation that has the form of an almost history-dependent variational inequality for the displacement field. We demonstrate existence and uniqueness results of abstract almost history-dependent inclusion and variational inequality in the reflexive Orlicz–Sobolev space. Finally, we apply the abstract results to prove existence of the unique weak solution to the contact problems.

    更新日期:2020-01-04
  • The C1 persistence of heteroclinic repellers in Rn
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2019-12-31
    Yuanlong Chen; Xiaoying Wu

    In this paper, we show that if f is a C1-map from Rn into itself and has heteroclinic repellers, then g also has heteroclinic repellers with ‖f−g‖C1 being small enough and exhibits Devaney's chaos. The results demonstrate C1 structural stability of heteroclinic repellers in Euclidean spaces. In the end, we give some examples to illustrate our theoretical results.

    更新日期:2020-01-04
  • Linear factorization of hypercyclic functions for differential operators
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2019-12-31
    Kit C. Chan; Jakob Hofstad; David Walmsley

    On the Fréchet space of entire functions H(C), we show that every nonscalar continuous linear operator L:H(C)→H(C) which commutes with differentiation has a hypercyclic vector f(z) in the form of the infinite product of linear polynomials:f(z)=∏j=1∞(1−zaj), where each aj is a nonzero complex number.

    更新日期:2020-01-04
  • A topological characterization of dual strict convexity in Asplund spaces
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2019-12-30
    Richard J. Smith

    Let X be an Asplund space. We show that the existence of an equivalent norm on X having a strictly convex dual norm is equivalent to the dual unit sphere SX⁎ (equivalently X⁎) possessing a non-linear topological property called (⁎), which was introduced by J. Orihuela, S. Troyanski and the author.

    更新日期:2020-01-04
  • Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-02
    M. Chmara; J. Maksymiuk

    Using the Mountain Pass Theorem we show that the problem{ddtLv(t,u(t),u˙(t))=Lx(t,u(t),u˙(t)) for a.e. t∈[a,b]u(a)=u(b)=0 has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian L=F(t,x,v)+V(t,x)+〈f(t),x〉 with growth conditions determined by anisotropic G-function and some geometric conditions of Ambrosetti-Rabinowitz type.

    更新日期:2020-01-04
  • Quantitative stability of two-stage distributionally robust risk optimization problem with full random linear semi-definite recourse
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-03
    Sainan Zhang; Shaoyan Guo; Liwei Zhang; Hongwei Zhang

    In this paper, we study a distributionally robust risk optimization (DRRO) problem where the information on the probability distribution of the underlying random variables is incomplete. But it is possible to use partial information to construct an ambiguity set of probability distributions. In some cases, decision vector x may have a direct impact on the likelihood of the underlying random events that occur after the decision is taken, which motivates us to propose an ambiguity set to be parametric and decision-dependent. To conduct quantitative stability analysis of the optimal value function and the optimal solution mapping of the DRRO problem, we derive error bounds results for the parametrized ambiguity set under the total variation metric and investigate Lipschitz continuity of the objective function of the DRRO problem under some conditions. As an application, we demonstrate that the two-stage stochastic linear semi-definite programs satisfy these conditions and then apply results obtained to it.

    更新日期:2020-01-04
  • On M-decomposable sets
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-03
    Valeriu Soltan

    According to Goberna, González, Martínez-Legaz, and Todorov (2010), an M-decomposable set in Rn is a closed convex set which is the sum of a compact convex set and a closed convex cone. Complementing the existing results on M-decomposable sets, we study their extreme, exposed, and asymptotic properties. Also, we consider M-polyhedral sets which are sums of compact convex sets and polyhedral cones and establish some characteristic properties of such sets.

    更新日期:2020-01-04
  • On the nonstationary Stokes system in a cone: Asymptotics of solutions at infinity
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-03
    Vladimir Kozlov; Jürgen Rossmann

    The paper deals with the Dirichlet problem for the nonstationary Stokes system in a cone. The authors obtain existence and uniqueness results for solutions in weighted Sobolev spaces and study the asymptotics of the solutions at infinity.

    更新日期:2020-01-04
  • Support theorems for the transverse ray transform of tensor fields of rank m
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-03
    Anuj Abhishek

    Let m and n be integers satisfying m≥2 and n≥m+2. Let (M,g) be a simple, real analytic, Riemannian manifold of dimension n with boundary and f be a rank m-tensor field defined over it. In this work, we prove a support theorem for the transverse ray transform of such tensor fields. More specifically, we prove that for a tensor field f of rank m, if the transverse ray transform of f vanishes over an appropriate open set of maximal geodesics of M, then the support of f vanishes on the points of M that lie on the union of the aforementioned open set of geodesics. We also show that if the tensor field is assumed to be symmetric, then one has a similar support theorem for the transverse ray transform of symmetric tensor fields of rank up to n−1.

    更新日期:2020-01-04
  • Weighted variation inequalities for singular integrals and commutators
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-03
    Yongming Wen; Huoxiong Wu; Jing Zhang

    In this paper, we extend the mixed weak-type inequalities of Sawyer type for Calderon-Zygmund operators to the variation operators of θ-type Calderon-Zygmund operators. Moreover, the corresponding quantitative weighted bounds as well as the weighted estimates in the extreme case p=∞ are also obtained. Meanwhile, we also present the quantitative Bloom type estimate and Cp estimates for variation operators of commutators.

    更新日期:2020-01-04
  • The weak⁎ density in operator ideals
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-03
    Ju Myung Kim

    Given a finitely generated tensor norm α, we investigate weak⁎ densities of adjoint operators in the Banach operator ideal A associated with α. We also study relations between the α-approximation properties and weak⁎ densities of finite rank adjoint operators in A. Some examples are given satisfying that all adjoint operators are not weak⁎ dense in the ideal of compact operators.

    更新日期:2020-01-04
  • On the convergence of augmented Lagrangian method for optimal transport between nonnegative densities
    J. Math. Anal. Appl. (IF 1.188) Pub Date : 2020-01-03
    Romain Hug; Emmanuel Maitre; Nicolas Papadakis

    The dynamical formulation of the optimal transport problem, introduced by J. D. Benamou and Y. Brenier [4], amounts to find a time dependent space density and velocity field minimizing a transport energy between two densities. In order to solve this problem, an algorithm has been proposed to estimate the saddle point of a Lagrangian. We study the convergence of this algorithm in the most general case where initial and final densities may vanish on regions of the transportation domain. Under these assumptions, the main difficulty of our study is the proof of existence of a saddle point and of uniqueness of the density-momentum component, as it leads to deal with non-regular optimal transportation maps. For these reasons, a detailed study of the regularity properties of the velocity field associated to an optimal transportation map is required.

    更新日期:2020-01-04
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