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Approximation diffusion for the Nonlinear Schrödinger equation with a random potential Asymptot. Anal. (IF 1.4) Pub Date : 2024-01-29 Grégoire Barrué, Arnaud Debussche, Maxime Tusseau
We prove that the stochastic Nonlinear Schrödinger (NLS) equation is the limit of NLS equation with random potential with vanishing correlation length. We generalize the perturbed test function method to the context of dispersive equations. Apart from the difficulty of working in infinite dimension, we treat the case of random perturbations which are not assumed uniformly bounded.
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Bound states of weakly deformed soft waveguides Asymptot. Anal. (IF 1.4) Pub Date : 2024-01-24 Pavel Exner, Sylwia Kondej, Vladimir Lotoreichik
In this paper we consider the two-dimensional Schrödinger operator with an attractive potential which is a multiple of the characteristic function of an unbounded strip-shaped region, whose thickness is varying and is determined by the function R∋x↦d+εf(x), where d>0 is a constant, ε>0 is a small parameter, and f is a compactly supported continuous function. We prove that if ∫Rfdx>0, then the respective
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New decay results for Timoshenko system in the light of the second spectrum of frequency with infinite memory and nonlinear damping of variable exponent type Asymptot. Anal. (IF 1.4) Pub Date : 2024-01-24 Adel M. Al-Mahdi
In this study, we consider a one-dimensional Timoshenko system with two damping terms in the context of the second frequency spectrum. One damping is viscoelastic with infinite memory, while the other is a non-linear frictional damping of variable exponent type. These damping terms are simultaneously and complementary acting on the shear force in the domain. We establish, for the first time to the
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On a biharmonic coupled system with non-standard nonlinearity: Existence, blow up and numerics Asymptot. Anal. (IF 1.4) Pub Date : 2024-01-16 Oulia Bouhoufani, Salim A. Messaoudi, Mohamed Alahyane
In this paper, we consider a coupled system of two biharmonic equations with damping and source terms of variable-exponent nonlinearities, supplemented with initial and mixed boundary conditions. We establish an existence and uniqueness result of a weak solution, under suitable assumptions on the variable exponents. Then, we show that solutions with negative-initial energy blow up in finite time. To
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Recovery of a general nonlinearity in the semilinear wave equation Asymptot. Anal. (IF 1.4) Pub Date : 2024-01-02 Antônio Sá Barreto, Plamen Stefanov
We study the inverse problem of recovery a nonlinearity f(t,x,u), which is compactly supported in x, in the semilinear wave equation utt−Δu+f(t,x,u)=0. We probe the medium with either complex or real-valued harmonic waves of wavelength ∼h and amplitude ∼1. They propagate in a regime where the nonlinearity affects the subprincipal but not the principal term, except for the zeroth harmonics. We measure
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Existence and regularity of solutions of nonlinear anisotropic elliptic problem with Hardy potential Asymptot. Anal. (IF 1.4) Pub Date : 2023-12-22 Hichem Khelifi
In this paper, we are interested in the existence and regularity of solutions for some anisotropic elliptic equations with Hardy potential and Lm(Ω) data in appropriate anisotropic Sobolev spaces. The aim of this work is to get natural conditions to show the existence and regularity results for thesolutions, that is related to an anisotropic Hardy inequality.
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Polynomial stability of thermoelastic Timoshenko system with non-global time-delayed Cattaneo’s law Asymptot. Anal. (IF 1.4) Pub Date : 2023-12-21 Haidar Badawi, Hawraa Alsayed
In this paper, we consider a one dimensional thermoelastic Timoshenko system in which the heat flux is given by Cattaneo’s law and acts locally on the bending moment with a time delay. We prove its well-posedness, strong stability, and polynomial stability.
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Long-time behavior of nonclassical diffusion equations with memory on time-dependent spaces Asymptot. Anal. (IF 1.4) Pub Date : 2023-12-12 Jiangwei Zhang, Zhe Xie, Yongqin Xie
This paper aims to study the long-time behavior of nonclassical diffusion equation with memory and disturbance parameters on time-dependent space. By using the contractive process method on the family of time-dependent spaces and operator decomposition technique, the existence of pullback attractors is first proved. Then the upper semi-continuity of pullback attractors with respect to perturbation
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Approximation of Dirichlet-to-Neumann operator for a planar thin layer and stabilization in the framework of couple stress elasticity with voids Asymptot. Anal. (IF 1.4) Pub Date : 2023-12-08 Athmane Abdallaoui, Abdelkarim Kelleche
In this paper, we start from a two dimensional transmission model problem in the framework of couple stress elasticity with voids which is defined in a fixed domain Ω− juxtaposed with a planar thin layer Ω+δ. We first derive a first approximation of Dirichlet-to-Neumann operator for the thin layerΩ+δ by using the techniques of asymptotic expansion with scaling, which allows us to approximate the transmission
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Semiclassical WKB problem for the non-self-adjoint Dirac operator with a multi-humped decaying potential Asymptot. Anal. (IF 1.4) Pub Date : 2023-12-06 Nicholas Hatzizisis, Spyridon Kamvissis
In this paper we study the semiclassical behavior of the scattering data of a non-self-adjoint Dirac operator with a real, positive, multi-humped, fairly smooth but not necessarily analytic potential decaying at infinity. We provide the rigorous semiclassical analysis of the Bohr-Sommerfeld condition for the location of the eigenvalues, the norming constants, and the reflection coefficient.
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Asymptotic decay towards steady states of solutions to very fast and singular diffusion equations Asymptot. Anal. (IF 1.4) Pub Date : 2023-12-01 Georgy Kitavtsev, Roman M. Taranets
We analyze long-time behavior of solutions to a class of problems related to very fast and singular diffusion porous medium equations having non-homogeneous in space and time source terms with zero mean. In dimensions two and three, we determine critical values of porous medium exponent for the asymptotic H1-convergence of the solutions to a unique non-homogeneous positive steady state generally to
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Fractal dimension of global attractors for a Kirchhoff wave equation with a strong damping and a memory term Asymptot. Anal. (IF 1.4) Pub Date : 2023-11-28 Yuming Qin, Hongli Wang, Bin Yang
This paper is concerned with the dimension of the global attractors for a time-dependent strongly damped subcritical Kirchhoff wave equation with a memory term. A careful analysis is required in the proof of a stabilizability inequality. The main result establishes the finite dimensionality of theglobal attractor.
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Optimal stability for laminated beams with Kelvin–Voigt damping and Fourier’s law Asymptot. Anal. (IF 1.4) Pub Date : 2023-11-28 Victor Cabanillas Zannini, Teófanes Quispe Méndez, A.J.A. Ramos
This article deals with the asymptotic behavior of a mathematical model for laminated beams with Kelvin–Voigt dissipation acting on the equations of transverse displacement and dimensionless slip. We prove that the evolution semigroup is exponentially stable if the damping is effective in the two equations of the model. Otherwise, we prove that the semigroup is polynomially stable and find the optimal
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Homogenization of an eigenvalue problem through rough surfaces Asymptot. Anal. (IF 1.4) Pub Date : 2023-11-15 Jake Avila, Sara Monsurrò, Federica Raimondi
In a bounded cylinder with a rough interface we study the asymptotic behaviour of the spectrum and its associated eigenspaces for a stationary heat propagation problem. The main novelty concerns the proof of the uniform a priori estimates for the eigenvalues. In fact, due to the peculiar geometry of the domain, standard techniques do not apply and a suitable new approach is developed.
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On a class of infinite semipositone problems for (p,q) Laplace operator Asymptot. Anal. (IF 1.4) Pub Date : 2023-11-15 R. Dhanya, Sarbani Pramanik, R. Harish
We analyze a non-linear elliptic boundary value problem that involves (p,q) Laplace operator, for the existence of its positive solution in an arbitrary smooth bounded domain. The non-linearity here is driven by a singular, monotonically increasing continuous function in (0,∞) which is eventually positive. The novelty in proving the existence of a positive solution lies in the construction of a suitable
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Behaviour of large eigenvalues for the asymmetric quantum Rabi model Asymptot. Anal. (IF 1.4) Pub Date : 2023-11-15 Mirna Charif, Ahmad Fino, Lech Zielinski
We prove that the spectrum of the asymmetric quantum Rabi model consists of two eigenvalue sequences (Em+)m=0∞, (Em−)m=0∞, satisfying a two-term asymptotic formula with error estimate of the form O(m−1/4), when m tends to infinity.
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Long-time solvability for the 2D inviscid Boussinesq equations with borderline regularity and dispersive effects Asymptot. Anal. (IF 1.4) Pub Date : 2023-11-13 V. Angulo-Castillo, L.C.F. Ferreira, L. Kosloff
We are concerned with the long-time solvability for 2D inviscid Boussinesq equations for a larger class of initial data which covers the case of borderline regularity. First we show the local solvability in Besov spaces uniformly with respect to a parameter κ associated with the stratification of the fluid. Afterwards, employing a blow-up criterion and Strichartz-type estimates, the long-time solvability
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Approximate mixed synchronization by groups for a coupled system of wave equations Asymptot. Anal. (IF 1.4) Pub Date : 2023-11-10 Tatsien Li, Bopeng Rao
We first show that under a suitable balanced repartition of the mixed controls within the system, Kalman’s rank condition is still necessary and sufficient for the uniqueness of solution to the adjoint system associated with incomplete internal and boundary observations, therefore for the approximate controllability of the primary system by means of mixed controls. Then we study the stability of the
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Puiseux asymptotic expansions for convection-dominated transport problems in thin graph-like networks: Strong boundary interactions Asymptot. Anal. (IF 1.4) Pub Date : 2023-11-10 Taras Mel’nyk, Christian Rohde
This article completes the study of the influence of the intensity parameter α in the boundary condition ε∂νεuε−uεVε→·νε=εαφε given on the boundary of a thin three-dimensional graph-like network consisting of thin cylinders that are interconnected by small domains (nodes) with diameters of order O(ε). Inside of the thin network a time-dependent convection-diffusion equation with high Péclet number
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On periodic and compactly supported least energy solutions to semilinear elliptic equations with non-Lipschitz nonlinearity Asymptot. Anal. (IF 1.4) Pub Date : 2023-11-10 Jacques Giacomoni, Yavdat Il’yasov, Deepak Kumar
We discuss the existence and non-existence of periodic in one variable and compactly supported in the other variables least energy solutions for equations with non-Lipschitz nonlinearity of the form: −Δu=λup−uq in RN+1, where 0
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Spectrum, bifurcation and hypersurfaces of prescribed k-th mean curvature in Minkowski space Asymptot. Anal. (IF 1.4) Pub Date : 2023-11-10 Guowei Dai, Zhitao Zhang
By bifurcation and topological methods, we study the existence/nonexistence and multiplicity of one-sign or nodal solutions of the following k-th mean curvature problem in Minkowski spacetime rN−kv′1−v′2k′=λNCNkrN−1Hk(r,v)in (0,R),|v′|<1in (0,R),v′(0)=v(R)=0. As a previous step, we investigatethe spectral structure of its linearized problem at zero. Moreover, we also obtain a priori bounds and the
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Existence results for the Landau–Lifshitz–Baryakhtar equation Asymptot. Anal. (IF 1.4) Pub Date : 2023-11-10 C. Ayouch, D. Meskine, M. Tilioua
In this paper, the Landau–Lifshitz–Baryakhtar (LLBar) equation for magnetization dynamics in ferrimagnets is considered. We prove global existence of a periodic solutions as well as local existence and uniqueness of regular solutions. We also study the relationships between the Landau–Lifshitz–Baryakhtar equation and both Landau–Lifshitz–Bloch and harmonic map equations.
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Fractional diffusion for Fokker–Planck equation with heavy tail equilibrium: An à la Koch spectral method in any dimension Asymptot. Anal. (IF 1.4) Pub Date : 2023-10-24 Dahmane Dechicha, Marjolaine Puel
In this paper, we extend the spectral method developed (Dechicha and Puel (2023)) to any dimension d⩾1, in order to construct an eigen-solution for the Fokker–Planck operator with heavy tail equilibria, of the form (1+|v|2)−β2, in the range β∈]d,d+4[. The method developed in dimension 1 was inspired by the work of H. Koch on nonlinear KdV equation (Nonlinearity 28 (2015) 545). The strategy in this
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Semiclassical resolvent bounds for short range L∞ potentials with singularities at the origin Asymptot. Anal. (IF 1.4) Pub Date : 2023-10-23 Jacob Shapiro
We consider, for h,E>0, resolvent estimates for the semiclassical Schrödinger operator −h2Δ+V−E. Near infinity, the potential takes the form V=VL+VS, where VL is a long range potential which is Lipschitz with respect to the radial variable, while VS=O(|x|−1(log|x|)−ρ) for some ρ>1. Near the origin,|V| may behave like |x|−β, provided 0⩽β<2(3−1). We find that, for any ρ˜>1, there are C,h0>0 such that
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Higher order evolution inequalities involving Leray–Hardy potential singular on the boundary Asymptot. Anal. (IF 1.4) Pub Date : 2023-10-16 Mohamed Jleli, Bessem Samet, Calogero Vetro
We consider a higher order (in time) evolution inequality posed in the half ball, under Dirichlet type boundary conditions. The involved elliptic operator is the sum of a Laplace differential operator and a Leray–Hardy potential with a singularity located at the boundary. Using a unified approach,we establish a sharp nonexistence result for the evolution inequalities and hence for the corresponding
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Nodal solutions to (p,q)-Laplacian equations with critical growth Asymptot. Anal. (IF 1.4) Pub Date : 2023-10-16 Hongling Pu, Sihua Liang, Shuguan Ji
In this paper, a class of (p,q)-Laplacian equations with critical growth is taken into consideration: −Δpu−Δqu+(|u|p−2+|u|q−2)u+λϕ|u|q−2u=μg(u)+|u|q∗−2u,x∈R3,−Δϕ=|u|q,x∈R3, where Δξu=div(|∇u|ξ−2∇u) is the ξ-Laplacian operator (ξ=p,q), 32
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A Jacobi spectral method for calculating fractional derivative based on mollification regularization Asymptot. Anal. (IF 1.4) Pub Date : 2023-10-13 Wen Zhang, Changxing Wu, Zhousheng Ruan, Shufang Qiu
In this article, we construct a Jacobi spectral collocation scheme to approximate the Caputo fractional derivative based on Jacobi–Gauss quadrature. The convergence analysis is provided in anisotropic Jacobi-weighted Sobolev spaces. Furthermore, the convergence rate is presented for solving Caputofractional derivative with noisy data by invoking the mollification regularization method. Lastly, numerical
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Homogenization of distributive optimal control problem governed by Stokes system in an oscillating domain Asymptot. Anal. (IF 1.4) Pub Date : 2023-10-06 Swati Garg, Bidhan Chandra Sardar
The present article deals with the homogenization of a distributive optimal control problem (OCP) subjected to the more generalized stationary Stokes equation involving unidirectional oscillating coefficients posed in a two-dimensional oscillating domain. The cost functional considered is of the Dirichlet type involving a unidirectional oscillating coefficient matrix. We characterize the optimal control
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Some remarks on simplified double porosity model of immiscible incompressible two-phase flow Asymptot. Anal. (IF 1.4) Pub Date : 2023-10-06 M. Jurak, L. Pankratov, A. Vrbaški
The paper is devoted to the derivation, by linearization, of simplified homogenized models of an immiscible incompressible two-phase flow in double porosity media in the case of thin fissures. In a simplified double porosity model derived previously by the authors the matrix-fracture source term isapproximated by a convolution type source term. This approach enables to exclude the cell problem, in
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On the distribution of Born transmission eigenvalues in the complex plane Asymptot. Anal. (IF 1.4) Pub Date : 2023-09-29 Narek Hovsepyan
We analyze an approximate interior transmission eigenvalue problem in Rd for d=2 or d=3, motivated by the transmission problem of a transformation optics-based cloaking scheme and obtained by replacing the refractive index with its first order approximation, which is an unbounded function. Using the radial symmetry we show the existence of (infinitely many) complex transmission eigenvalues and prove
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The Euler–Poisswell/Darwin equation and the asymptotic hierarchy of the Euler–Maxwell equation Asymptot. Anal. (IF 1.4) Pub Date : 2023-09-25 Jakob Möller, Norbert J. Mauser
In this paper we introduce the (unipolar) pressureless Euler–Poisswell equation for electrons as the O(1/c) semi-relativistic approximation and the (unipolar) pressureless Euler–Darwin equation as the O(1/c2) semi-relativistic approximation of the (unipolar) pressureless Euler–Maxwell equation. Inthe “infinity-ion-mass” limit, the unipolar Euler–Maxwell equation arises from the bipolar Euler–Maxwell
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The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary Asymptot. Anal. (IF 1.4) Pub Date : 2023-09-11 Yoshikazu Giga, Michał Łasica, Piotr Rybka
We derive the dynamic boundary condition for the heat equation as a limit of boundary layer problems. We study convergence of their weak and strong solutions as the width of the layer tends to zero. We also discuss Γ-convergence of the functionals generating these flows. Our analysis of strong solutions depends on a new version of the Reilly identity.
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Global regularity for Oldroyd-B model with only stress tensor dissipation Asymptot. Anal. (IF 1.4) Pub Date : 2023-09-08 Weixun Feng, Zhi Chen, Dongdong Qin, Xianhua Tang
In this paper, we consider the d-dimensional (d⩾2) Oldroyd-B model with only dissipation in the equation of stress tensor, and establish a small data global well-posedness result in critical Lp framework. Particularly, we give a positive answer to the problem proposed recently by Wu-Zhao (J. Differ. Equ. 316 (2022)) involving the upper bound for the time integral of the lower frequency piece of the
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Existence of quasilinear elliptic equations with prescribed limiting behavior Asymptot. Anal. (IF 1.4) Pub Date : 2023-09-01 H. Ibrahim, R. Younes
We consider quasilinear elliptic equations Δpu+f(u)=0 in the quarter-plane Ω, with zero Dirichlet data. For some general nonlinearities f, we prove the existence of a positive solution with a prescribed limiting profile. The question is motivated by the result in (Adv. Nonlinear Stud. 13(1) (2013)115–136), where the authors establish that for solutions u(x1,x2) of the preceding Dirichlet problem, limx1→∞u(x1
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Concavity principles for nonautonomous elliptic equations and applications Asymptot. Anal. (IF 1.4) Pub Date : 2023-08-31 Nouf Almousa, Claudia Bucur, Roberta Cornale, Marco Squassina
In the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the space variable. In this paper we obtain new results aiming to get almost concavity results for a relevant class of anisotropic semilinear elliptic problems with spatially dependent source and diffusion.
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Global existence and asymptotic behaviour for a viscoelastic plate equation with nonlinear damping and logarithmic nonlinearity Asymptot. Anal. (IF 1.4) Pub Date : 2023-08-30 Bhargav Kumar Kakumani, Suman Prabha Yadav
In this article, we consider a viscoelastic plate equation with a logarithmic nonlinearity in the presence of nonlinear frictional damping term. Here we prove the existence of the solution to the problem using the Faedo–Galerkin method. Also, we prove few general decay rate results.
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A note on the one-dimensional critical points of the Ambrosio–Tortorelli functional Asymptot. Anal. (IF 1.4) Pub Date : 2023-08-29 Jean-François Babadjian, Vincent Millot, Rémy Rodiac
This note addresses the question of convergence of critical points of the Ambrosio–Tortorelli functional in the one-dimensional case under pure Dirichlet boundary conditions. An asymptotic analysis argument shows the convergence to two possible limits points: either a globally affine function or astep function with a single jump at the middle point of the space interval, which are both critical points
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Rigidity and nonexistence of complete hypersurfaces via Liouville type results and other maximum principles, with applications to entire graphs Asymptot. Anal. (IF 1.4) Pub Date : 2023-08-23 Railane Antonia, Giovanni Molica Bisci, Henrique F. de Lima, Márcio S. Santos
We investigate complete hypersurfaces with some positive higher order mean curvature in a semi-Riemannian warped product space. Under standard curvature conditions on the ambient space and appropriate constraints on the higher order mean curvatures, we establish rigidity and nonexistence results via Liouville type results and suitable maximum principles related to the divergence of smooth vector fields
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Comparison results for a nonlocal singular elliptic problem Asymptot. Anal. (IF 1.4) Pub Date : 2023-08-23 Barbara Brandolini, Ida de Bonis, Vincenzo Ferone, Bruno Volzone
We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are presented, depending on the summability of the right-hand side of the equation. The maximum principle arguments employed in the core of the proofs of the main results
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Stabilization for the Klein–Gordon–Zakharov system Asymptot. Anal. (IF 1.4) Pub Date : 2023-08-18 Weijia Li, Yuqi Shangguan, Weiping Yan
This paper deals with global stability dynamics for the Klein–Gordon–Zakharov system in R2. We first establish that this system admits a family of linear mode unstable explicit quasi-periodic wave solutions. Next, we prove that the Kelvin–Voigt damping can help to stabilize those linear mode unstable explicit quasi-periodic wave solutions for the Klein–Gordon–Zakharov system in the Sobolev space H
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Semilinear hyperbolic inequalities with Hardy potential in a bounded domain Asymptot. Anal. (IF 1.4) Pub Date : 2023-08-11 Mohamed Jleli, Bessem Samet
We consider hyperbolic inequalities with Hardy potential utt−Δu+λ|x|2u⩾|x|−a|u|pin (0,∞)×B1∖{0},u(t,x)⩾f(x)on (0,∞)×∂B1, where B1 is the unit ball in RN, N⩾3, λ>−(N−22)2, a⩾0, p>1 and f is a nontrivial L1-function. We study separately the cases: λ=0, −(N−22)2<λ<0 and λ>0. For each case, we obtain an optimal criterium for the nonexistence of weak solutions. Our study yields naturally optimal nonexistence
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Topological sensitivity analysis for the 3D nonlinear Navier–Stokes equations Asymptot. Anal. (IF 1.4) Pub Date : 2023-08-11 Maatoug Hassine, Marwa Ouni
This work is devoted to a topological asymptotic expansion for the nonlinear Navier–Stokes operator. We consider the 3D Navier–Stokes equations as a model problem and we derive a topological sensitivity analysis for a design function with respect to the insertion of a small obstacle inside the fluid flow domain. The asymptotic behavior of the perturbed velocity field with respect to the obstacle size
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Semiclassical states for coupled nonlinear Schrödinger equations with critical frequency Asymptot. Anal. (IF 1.4) Pub Date : 2023-08-04 Taiyong Chen, Yahui Jiang, Marco Squassina, Jianjun Zhang
In this paper, we are concerned with the coupled nonlinear Schrödinger system −ε2Δu+a(x)u=μ1u3+βv2uin RN,−ε2Δv+b(x)v=μ2v3+βu2vin RN, where 1⩽N⩽3, μ1,μ2,β>0, a(x) and b(x) are nonnegative continuous potentials, and ε>0 is a small parameter. We show the existence of positive ground state solutions for the system above and also establish the concentration behaviour as ε→0, when a(x) and b(x) achieve 0
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Singular behavior for a multi-parameter periodic Dirichlet problem Asymptot. Anal. (IF 1.4) Pub Date : 2023-08-04 Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino
We consider a Dirichlet problem for the Poisson equation in a periodically perforated domain. The geometry of the domain is controlled by two parameters: a real number ϵ>0, proportional to the radius of the holes, and a map ϕ, which models the shape of the holes. So, if g denotes the Dirichlet boundary datum and f the Poisson datum, we have a solution for each quadruple (ϵ,ϕ,g,f). Our aim is to study
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Singular elliptic problem involving a Hardy potential and lower order term Asymptot. Anal. (IF 1.4) Pub Date : 2023-08-04 Abdelaaziz Sbai, Youssef El Hadfi, Mounim El Ouardy
We consider the following non-linear singular elliptic problem (1)−div(M(x)|∇u|p−2∇u)+b|u|r−2u=aup−1|x|p+fuγin Ωu>0in Ωu=0on ∂Ω, where 10,0⩽f∈Lm(Ω) and 1
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Error estimates for Gaussian beams at a fold caustic Asymptot. Anal. (IF 1.4) Pub Date : 2023-07-18 Olivier Lafitte, Olof Runborg
In this work we show an error estimate for a first order Gaussian beam at a fold caustic, approximating time-harmonic waves governed by the Helmholtz equation. For the caustic that we study the exact solution can be constructed using Airy functions and there are explicit formulae for the Gaussian beam parameters. Via precise comparisons we show that the pointwise error on the caustic is of the order
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How hysteresis produces discontinuous patterns in degenerate reaction–diffusion systems Asymptot. Anal. (IF 1.4) Pub Date : 2023-07-12 Guillaume Cantin
In this paper, we study the asymptotic behaviour of the solutions to a degenerate reaction–diffusion system. This system admits a continuum of discontinuous stationary solutions due to the effect of a hysteresis process, but only one discontinuous stationary solution is compatible with a principleof preservation of locally invariant regions. Using a macroscopic mass effect which guarantees that fast
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Existence and convergence of the least energy sign-changing solutions for nonlinear Kirchhoff equations on locally finite graphs Asymptot. Anal. (IF 1.4) Pub Date : 2023-07-12 Guofu Pan, Chao Ji
In this paper, we study the least energy sign-changing solutions to the following nonlinear Kirchhoff equation −(a+b∫V|∇u|2dμ)Δu+c(x)u=f(u) on a locally finite graph G=(V,E), where a, b are positive constants. We use the constrained variational method to prove the existence of a least energy sign-changing solution ub of the above equation if c(x) and f satisfy certain assumptions, and to show the energy
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Existence of nontrivial solution for quasilinear equations involving the 1-biharmonic operator Asymptot. Anal. (IF 1.4) Pub Date : 2023-07-12 Huo Tao, Lin Li, Xiao-Qiong Yang
In this paper, we study the existence results of a quasilinear elliptic problem involving the 1-biharmonic operator in RN, whose nonlinearity satisfies appropriate conditions. The existence theorem is proved through a new version of the Mountain Pass Theorem to locally Lipschitz functionals, whereit is considered the Cerami compactness condition rather than the Palais–Smale one.
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Well-posedness and polynomial energy decay rate of a transmission problem for Rayleigh beam model with heat conduction Asymptot. Anal. (IF 1.4) Pub Date : 2023-07-14 Mohammad Akil, Mouhammad Ghader, Zayd Hajjej, Mohamad Ali Sammoury
In this paper, we investigate the stability of the transmission problem for Rayleigh beam model with heat conduction. First, we reformulate our system into an evolution equation and prove our problem’s well-posedness. Next, we demonstrate the resolvent of the operator is compact in the energy space, then by using the general criteria of Arendt–Batty, we prove that the thermal dissipation is enough
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Arched beams of Bresse type: New thermal couplings and pattern of stability Asymptot. Anal. (IF 1.4) Pub Date : 2023-06-30 G.E. Bittencourt Moraes, S.J. de Camargo, M.A. Jorge Silva
This is the second paper of a trilogy intended by the authors in what concerns a unified approach to the stability of thermoelastic arched beams of Bresse type under Fourier’s law. Differently of the first one, where the thermal couplings are regarded on the axial and bending displacements, here the thermal couplings are taken over the shear and bending forces. Such thermal effects still result in
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On the asymptotic behavior of the energy for evolution models with oscillating time-dependent damping Asymptot. Anal. (IF 1.4) Pub Date : 2023-06-30 Halit Sevki Aslan, Marcelo Rempel Ebert
In the present paper, we study the influence of oscillations of the time-dependent damping term b(t)ut on the asymptotic behavior of the energy for solutions to the Cauchy problem for a σ-evolution equation utt+(−Δ)σu+b(t)ut=0,(t,x)∈[0,∞)×Rn,u(0,x)=u0(x),ut(0,x)=u1(x),x∈Rn, where σ>0 and b is acontinuous and positive function. Mainly we consider damping terms that are perturbations of the scale invariant
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On the semi-classical analysis of Schrödinger operators with linear electric potentials on a bounded domain Asymptot. Anal. (IF 1.4) Pub Date : 2023-06-30 Rayan Fahs
The aim of this paper is to establish the asymptotic expansion of the eigenvalues of the Stark Hamiltonian, with a strong uniform electric field and Dirichlet boundary conditions on a smooth bounded domain of RN, N⩾2. This work aims at generalizing the recent results of Cornean, Krejčiřik, Pedersen, Raymond, and Stockmeyer in dimension 2. More precisely, in dimension N, in the strong electric field
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Bifurcation and stability for charged drops Asymptot. Anal. (IF 1.4) Pub Date : 2023-06-29 Guowei Dai, Ben Duan, Fang Liu
In this paper, we investigate the Laplace’s equation for the electrical potential of charge drops on exterior domain, and overdetermined boundary conditions are prescribed. We determine the local bifurcation structure with respect to the surface tension coefficient as bifurcation parameter. Furthermore, we establish the stability and the instability near the bifurcation point.
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On the hyperbolic relaxation of the Cahn–Hilliard equation with a mass source Asymptot. Anal. (IF 1.4) Pub Date : 2023-06-14 Dieunel Dor
In this paper, we consider the hyperbolic Cahn–Hilliard equation with a proliferation term, which has applications in biology. First, we study the well-posedness and the regularity of the solutions, which then allow us to study the dissipativity and the high-order dissipativity and finally the existence of the exponential attractor with Dirichlet boundary conditions. Finally, we give numerical simulations
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Global attractors for a partially damped Timoshenko–Ehrenfest system without the hypothesis of equal wave speeds Asymptot. Anal. (IF 1.4) Pub Date : 2023-06-07 M.M. Freitas, D.S. Almeida Júnior, L.G.R. Miranda, A.J.A. Ramos, R.Q. Caljaro
This paper is concerned with the study of global attractors for a new semilinear Timoshenko–Ehrenfest type system. Firstly we establish the well-posedness of the system using Faedo–Galerkin method. By considering only one damping term acting on the vertical displacement, we prove the existence of asmooth finite dimensional global attractor using the recent quasi-stability theory. Our results holds
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Vortex rigid motion in quasi-geostrophic shallow-water equations Asymptot. Anal. (IF 1.4) Pub Date : 2023-06-02 Emeric Roulley
In this paper, we prove the existence of analytic relative equilibria with holes for quasi-geostrophic shallow-water equations. More precisely, using bifurcation techniques, we establish for any m large enough the existence of two branches of m-fold doubly-connected V-states bifurcating from any annulus of arbitrary size.
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Rigorous derivation of the Fick cross-diffusion system from the multi-species Boltzmann equation in the diffusive scaling Asymptot. Anal. (IF 1.4) Pub Date : 2023-06-01 Marc Briant, Bérénice Grec
We present the arising of the Fick cross-diffusion system of equations for fluid mixtures from the multi-species Boltzmann equation in a rigorous manner in Sobolev spaces. To this end, we formally show that, in a diffusive scaling, the hydrodynamical limit of the kinetic system is the Fick model supplemented with a closure relation and we give explicit formulae for the macroscopic diffusion coefficients
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Dynamics and robustness for the 2D Navier–Stokes equations with multi-delays in Lipschitz-like domains Asymptot. Anal. (IF 1.4) Pub Date : 2023-05-31 Keqin Su, Xin-Guang Yang, Alain Miranville, He Yang
This paper is concerned with the dynamics of the two-dimensional Navier–Stokes equations with multi-delays in a Lipschitz-like domain, subject to inhomogeneous Dirichlet boundary conditions. The regularity of global solutions and of pullback attractors, based on tempered universes, is established,extending the results of Yang, Wang, Yan and Miranville (Discrete Contin. Dyn. Syst. 41 (2021) 3343–3366)
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On the spectral gap of higher-dimensional Schrödinger operators on large domains Asymptot. Anal. (IF 1.4) Pub Date : 2023-05-03 Joachim Kerner, Matthias Täufer
We study the asymptotic behaviour of the spectral gap of Schrödinger operators in two and higher dimensions and in a limit where the volume of the domain tends to infinity. Depending on properties of the underlying potential, we will find different asymptotic behaviours of the gap. In some cases the gap behaves as the gap of the free Dirichlet Laplacian and in some cases it does not.