The existence of global BV solutions for the Aw-Rascle system with linear damping is considered. In order to get approximate solutions we consider the system in Lagrangian coordinates, then by using the wave front tracking method coupling with and suitable splitting algorithm and the ideas of [1] we get a sequence of approximate solutions. Finally we show the convergence of this approximate sequence

In this paper we prove the local well-posedness of strong solutions to a chemotaxis-shallow water system with initial vacuum in a bounded domain Ω ų ℝ2 without the standard compatibility condition for the initial data. This improves some results obtained in [J. Differential Equations 261(2016), 6758–6789].

In this article, we solve completely Gleason’s problem on Fock-Sobolev spaces Fp,m for any non-negative integer m and 0 < p ≤ ∞.

For high-dimensional models with a focus on classification performance, the ℓ1-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data. We propose two types of weighted Lasso estimates, depending upon covariates determined by the McDiarmid inequality. Given

This article explores the characteristics of the average abundance function with mutation on the basis of the multi-player snowdrift evolutionary game model by analytical analysis and numerical simulation. The specific field of this research concerns the approximate expressions of the average abundance function with mutation on the basis of different levels of selection intensity and an analysis of

In this article, we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities. Firstly, we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality, the Poincaré inequality, and the Hardy inequality. Then, by using the potential well method and the inequality

Let L:= −Δ + V be the Schrödinger operator on ℝn with n ≥ 3, where V is a non-negative potential satisfying Δ−1 (V) ∈ L∞(ℝn). Let w be an L-harmonic function, determined by V, satisfying that there exists a positive constant ö such that, for any x ∈ ℝn, 0 < δ ≤ w(x) ≤ 1. Assume that p(·): ℝn → (0, 1] is a variable exponent satisfying the globally log-Hölder continuous condition. In this article, the

Most results on the polynomial-like iterative equation are given under the condition that the given function is monotone, while a work by L. Liu and X. Gong gets non-monotone PM solutions with height 1 when the given function is of the same case. Removing the condition on height for the given function, we first give a method to assert the nonexistence of C0 solutions, then present equivalent conditions

Hilbert Problem 15 required an understanding of Schubert’s book [1], both its methods and its results. In this paper, following his idea, we prove that the formulas in §6, §7, §10, about the incidence of points, lines and planes, are all correct. As an application, we prove formulas 8 and 9 in §12, which are frequently used in his book.

In this article, we consider the Lipschitz metric of conservative weak solutions for the rotation-Camassa-Holm equation. Based on defining a Finsler-type norm on the tangent space for solutions, we first establish the Lipschitz metric for smooth solutions, then by proving the generic regularity result, we extend this metric to general weak solutions.

In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space \({\cal F}\dot {\cal N}_{p\left( \cdot \right),h\left( \cdot \right),q}^{s\left( \cdot \right)}\left( {{\mathbb{R}^3}} \right)\) with \(s\left( \cdot \right) = 4 - 2\alpha - {3 \over {p\left( \cdot \right)}}\). We prove global well-posedness result

In this paper we deal with the martingales in variable Lebesgue space over a probability space. We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space. The main aim of this paper is to investigate the boundedness of weak-type and strong-type Doob’s maximal operators in martingale Lebesgue

In this article, we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities. Furthermore, we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.

This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space. Utilizing the KKM theorem, a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established. By using a fixed point theorem for a condensing set-valued map, the nonemptiness and compactness of the set

In this article, we are concerned with analytical solutions for a model of inviscid liquid-gas two-phase flow. On the basis of Yuen’s works [25, 27–29] on self-similar solutions for compressible Euler equations, we present some special self-similar solutions for a model of inviscid liquid-gas two-phase flow in radial symmetry with and without rotation, and in elliptic symmetry without rotation. Some

This paper studies the mixed radial-angular integrability of parametric Marcinkiewicz integrals along “polynomial curves”. Under the assumption that the kernels satisfy certain rather weak size conditions on the unit sphere with radial roughness, the authors prove that such operators are bounded on the mixed radial-angular spaces. Meanwhile, corresponding vector-valued versions are also obtained.

In this paper, we consider an inflow problem for the non-isentropic Navier-Stokes-Poisson system in a half line (0, ∞). For the general gas including ideal polytropic gas, we first give some results for the existence of the stationary solution with the aid of center manifold theory on a 4 × 4 system of autonomous ordinary differential equations. We also show the time asymptotic stability of the stationary

In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate. The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models. We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that, via

The aim of this article is twofold. One aim is to establish the precise forms of Landau-Bloch type theorems for certain polyharmonic mappings in the unit disk by applying a geometric method. The other is to obtain the precise values of Bloch constants for certain log-p-harmonic mappings. These results improve upon the corresponding results given in Bai et al. (Complex Anal. Oper. Theory, 13(2): 321–340

Let A be an infinite dimensional stably finite unital simple separable C*-algebra. Let B ⊂ A be a stably (centrally) large subalgebra in A such that B is m-almost divisible (m-almost divisible, weakly (m, n)-divisible). Then A is 2(m + 1)-almost divisible (weakly m-almost divisible, secondly weakly (m, n)-divisible).

In this paper, we investigate the λ-nuclearity in the system of completely 1-summing mapping spaces (Π1(·, ·), π1). In Section 2, we obtain that ℂ is the unique operator space that is nuclear in the system (Π1(·, ·), π1). We generalize some results in Section 2 to λ-nuclearity in Section 3.

In this paper, the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data. The global existence and uniqueness of the strong solution in a hybrid Besov space are proved by using the Littlewood-Paley decomposition and Friedrichs’ regularization method.

In this article, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a = {aj}j≥1 and b = {bj}j≥1 of positive numbers. We obtain strong equivalences of the approximation numbers, and necessary and sufficient conditions on a, b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.

Although QP-free algorithms have good theoretical convergence and are effective in practice, their applications to minimax optimization have not yet been investigated. In this article, on the basis of the stationary conditions, without the exponential smooth function or constrained smooth transformation, we propose a QP-free algorithm for the nonlinear minimax optimization with inequality constraints

The theory of increasing and convex-along-rays (ICAR) functions defined on a convex cone in a real locally convex topological vector space X was already well developed. In this paper, we first examine abstract convexity of increasing plus-convex-along-rays (IPCAR) functions defined on a real normed linear space X. We also study, for this class of functions, some concepts of abstract convexity, such

This article is devoted to studying the initial-boundary value problem for an ideal polytropic model of non-viscous and compressible gas. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and give a rigorous proof of the asymptotic stability of both the degenerate boundary layer and its superposition with the 3-rarefaction wave under some smallness conditions

This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation. We obtain a critical value λ D1 (Ω0), and demonstrate that the existence of the predator in \({\overline \Omega _0}\) only depends on the relationship of the growth rate μ of the predator and λ D1 (Ω0), not on the prey. Furthermore, when μ < λ D1 (Ω0), we obtain the existence and uniqueness of

In this article we study the two-dimensional complete λ-translators immersed in the Euclidean space ℝ3 and Minkovski space ℝ31 . We obtain two classification theorems: one for two-dimensional complete λ-translators x: M2 → ℝ3 and one for two-dimensional complete space-like λ-translators x: M2 → ℝ31 , with a second fundamental form of constant length.

We show that the spatial Lq-norm (q > 5/3) of the vorticity of an incompressible viscous fluid in ℝ3 remains bounded uniformly in time, provided that the direction of vorticity is Hölder continuous in space, and that the space-time Lq-norm of vorticity is finite. The Hölder index depends only on q. This serves as a variant of the classical result by Constantin-Fefferman (Direction of vorticity and

In this paper, we consider the existence of nontrivial weak solutions to a double critical problem involving a fractional Laplacian with a Hardy term: $${( - \Delta )^s}u - \gamma {u \over {{{\left| x \right|}^{2s}}}} = {{{{\left| u \right|}^{2_s^ * (\beta ) - 2}}u} \over {{{\left| x \right|}^\beta }}} + \left[ {{I_\mu } * {F_\alpha }( \cdot ,u)} \right](x){f_\alpha }(x,u),\;\;\;\;u \in {\dot H^{^s}}({\mathbb{R}^n})

We prove that the group of weighted composition operators induced by continuous automorphism groups of the upper half plane \(\mathbb{U}\) is strongly continuous on the weighted Dirichlet space of \(\mathbb{U}\), \({{\cal D}_\alpha }(\mathbb{U})\). Further, we investigate when they are isometries on \({{\cal D}_\alpha }(\mathbb{U})\). In each case, we determine the semigroup properties while in the

In this article we consider the compressible viscous magnetohydrodynamic equations with Coulomb force. By spectral analysis and energy methods, we obtain the optimal time decay estimate of the solution. We show that the global classical solution converges to its equilibrium state at the same decay rate as the solution of the linearized equations.

In this article, we first give two simple examples to illustrate that two types of parametric representation of the family of Σ0K have some gaps. Then we also find that the area derivative formula (1.6), which is used to estimate the area distortion of Σ0K , cannot be derived from [6], but that formula still holds for Σ0K through our amendatory parametric representation for the one obtained by Eremenko

In this article, we study the following fractional (p, q)-Laplacian equations involving the critical Sobolev exponent: $$({P_{\mu ,\lambda }})\left\{ {\begin{array}{*{20}{l}} {( - \Delta )_p^{{s_1}}u + ( - \Delta )_q^{{s_2}}u = \mu |u{|^{q - 2}}u + \lambda |u{|^{p - 2}}u + |u{|^{p_{{s_1}}^* - 2}}u,}&{\text{in}\;\Omega ,} \\ {u = 0,}&{\text{in}\;{\mathbb{R}^N}\backslash \Omega ,} \end{array}} \right

Let K be the familiar class of normalized convex functions in the unit disk. In [14], Keogh and Merkes proved that for a function \(f(z) = z + \sum\limits_{k = 2}^\infty {{a_k}} {z^k}\) in the class K, $$\left| {{a_3} - \lambda a_2^2} \right| \le \max \left\{ {{1 \over 3},\left| {\lambda - 1} \right|} \right\},\;\;\;\;\lambda \in \mathbb{C}.$$ The above estimate is sharp for each λ. In this article

In this article, we study optimal reinsurance design. By employing the increasing convex functions as the admissible ceded loss functions and the distortion premium principle, we study and obtain the optimal reinsurance treaty by minimizing the VaR (value at risk) of the reinsurer’s total risk exposure. When the distortion premium principle is specified to be the expectation premium principle, we also

This article is devoted to a deep study of the Roper-Suffridge extension operator with special geometric properties. First, we prove that the Roper-Suffridge extension operator preserves ϵ starlikeness on the open unit ball of a complex Banach space ℂ × X, where X is a complex Banach space. This result includes many known results. Secondly, by introducing a new class of almost boundary starlike mappings

Let \({D_{{p_1},{p_2}, \cdots ,{p_n}}} = {\rm{\{ }}z \in {\mathbb{C}^n}{\rm{:}}\sum\limits_{l = 1}^n {{{\left| {{z_l}} \right|}^{{p_l}}} < 1{\rm{\} }},{p_l} > 1,l = 1,2, \cdots \;,n}.\). In this article, we first establish the sharp estimates of the main coefficients for a subclass of quasi-convex mappings (including quasi-convex mappings of type \(\mathbb{A}\) and quasi-convex mappings of type \(\mathbb{B}\))

In this paper, we study the coupled system of Kirchhoff type equations $$\left\{ {\matrix{ { - \left( {a + b\int_{{\mathbb{R}^3}} {{{\left| {\nabla u} \right|}^2}{\rm{d}}x} } \right)\Delta u + u = {{2\alpha } \over {\alpha + \beta }}{{\left| u \right|}^{\alpha - 2}}u{{\left| v \right|}^\beta },\;x \in {\mathbb{R}^3},} \hfill \cr { - \left( {a + b\int_{{\mathbb{R}^3}} {{{\left| {\nabla v} \right|}^2}{\rm{d}}x}

We show that the Weyl symbol of a Born-Jordan operator is in the same class as the Born-Jordan symbol, when Hörmander symbols and certain types of modulation spaces are used as symbol classes. We use these properties to carry over continuity, nuclearity and Schatten-von Neumann properties to the Born-Jordan calculus.

In this paper we obtain an Itô differential representation for a class of singular stochastic Volterra integral equations. As an application, we investigate the rate of convergence in the small time central limit theorem for the solution.

We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of order β ∈ (1/2, 3/4] is normal according to the values of β . We apply our results to two self-similar Gaussian processes: the subfractional Brownian motion and the bifractional Brownian motion.

In this paper, a stochastic multi-group AIDS model with saturated incidence rate is studied. We prove that the system is persistent in the mean under some parametric restrictions. We also obtain the sufficient condition for the existence of the ergodic stationary distribution of the system by constructing a suitable Lyapunov function. Our results indicate that the existence of ergodic stationary distribution

We investigate the following elliptic equations: $$\left\{ {\matrix{ { - M\left( {\int_{{\mathbb{R}^N}} {\phi ({{\left| {\nabla u} \right|}^2}){\rm{d}}x} } \right){\rm{div(}}\phi \prime ({{\left| {\nabla u} \right|}^2})\nabla u{\rm{) + }}{{\left| u \right|}^{\alpha - 2}}u = \lambda h(x,u),} \hfill \cr {u(x) \to 0,\;\;\;\;\;{\rm{as}}\left| x \right| \to \infty ,} \hfill \cr } } \right.\;\;\;\;\;\;\

In this article, we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrödinger type operator (−Δ)2 + V2 in ℝn(n ≥ 5) with V being a nonnegative potential satisfying the reverse Hölder inequality. Furthermore, we prove the boundedness of the variation operators on associated Morrey spaces. In the proof of the main results

The Editor-in-Chief has retracted this article [1], because one of the Editorial Board Mem- bers pointed out that Lemma 3.5 in [1] has an uncorrectable gap which can only be true when n = 1, 2, 3, indicating that the major theorem 1.1 in [1] is only a special case of Theorem 1 in [2], and Theorem 1.2 in [1] is only a trivial result in [3]. The author refused to retract the article [1] in his first

In this article, by the mean-integral of the conserved quantity, we prove that the one-dimensional non-isentropic gas dynamic equations in an ideal gas state do not possess a bounded invariant region. Moreover, we obtain a necessary condition on the state equations for the existence of an invariant region for a non-isentropic process. Finally, we provide a mathematical example showing that with a special

The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initial-boundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature

In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The weak convergence method plays an important role.

This article is devoted to establishing a least square based weak Galerkin method for second order elliptic equations in non-divergence form using a discrete weak Hessian operator. Naturally, the resulting linear system is symmetric and positive definite, and thus the algorithm is easy to implement and analyze. Convergence analysis in the H2 equivalent norm is established on an arbitrary shape regular

In 2018, Duan [1] studied the case of zero heat conductivity for a one-dimensional compressible micropolar fluid model. Due to the absence of heat conductivity, it is quite difficult to close the energy estimates. He considered the far-field states of the initial data to be constants; that is, \(\mathop {\lim }\limits_{x \to \pm \infty } ({v_0},{u_0},{\omega _0},{\theta _0})(x) = (1,0,0,1)\). He proved

We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture. When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave, it is shown that the viscous contact wave which corresponds to the contact discontinuity is asymptotically stable, provided the strength of contact

We study the existence and the regularity of solutions for a class of nonlocal equations involving the fractional Laplacian operator with singular nonlinearity and Radon measure data.

In this article, we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions. The initial vacuum is allowed.

We give characterizations for Bergman-Orlicz spaces with standard weights via a Lipschitz type condition in the Euclidean, hyperbolic, and pseudo-hyperbolic metrics. As an application, we obtain the boundeness of the symmetric lifting operator from Bergman-Orlicz spaces on the unit disk into Bergman-Orlicz spaces on the bidisk.

We study a Schrödinger system with the sum of linear and nonlinear couplings. Applying index theory, we obtain infinitely many solutions for the system with periodic potentials. Moreover, by using the concentration compactness method, we prove the existence and nonexistence of ground state solutions for the system with close-to-periodic potentials.

This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled system of nonlinear parabolic-elliptic equations completed by boundary and initial conditions. The main unknowns are the saltwater/freshwater interface depth and the freshwater hydraulic

In this article, we study the generalized quasilinear Schrödinger equation$$ - \text{div}({\varepsilon ^2}{g^2}(u)\nabla u) + {\varepsilon ^2}g(u)g'(u){\left| {\nabla u} \right|^2} + V(x)u = K(x){\left| u \right|^{p - 2}}u,\;\;\;\;x \in {\mathbb{R}^N},$$where N ≥ 3, ε> 0, 4

In this paper, we provide the boundedness property of the Riesz transforms associated to the Schrödinger operator \({\cal L} = \Delta + {\bf{V}}\) in a new weighted Morrey space which is the generalized version of many previous Morrey type spaces. The additional potential V considered in this paper is a non-negative function satisfying the suitable reverse Hölder’s inequality. Our results are new and

Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces. This complements earlier work [26] where we made a strong case for the assertion that statistical physics of regular systems should properly be based on the pair of Orlicz spaces 〈Lcosh−1, L log(L + 1)〉, since this framework gives a better description of regular observables, and also allows for a