Asymptotic Analysis - Volume 137, issue 3-4

Authors: Kitavtsev, Georgy | Taranets, Roman M.

Article Type: Research Article

Abstract: 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 H 1 -convergence of the solutions to a unique non-homogeneous positive steady state generally to hold.

Keywords: Asymptotic decay, steady states, porous medium, singular diffusion

DOI: 10.3233/ASY-231884

Citation: Asymptotic Analysis, vol. 137, no. 3-4, pp. 153-176, 2024

Authors: Hatzizisis, Nicholas | Kamvissis, Spyridon

Article Type: Research Article

Abstract: 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.

Keywords: Integral equations, operator theory, complex analysis, inverse scattering, Jost solutions, Wentzel–Kramers–Brillouin approximation, Schrödinger equation

DOI: 10.3233/ASY-231885

Citation: Asymptotic Analysis, vol. 137, no. 3-4, pp. 177-243, 2024

Authors: Abdallaoui, Athmane | Kelleche, Abdelkarim

Article Type: Research Article

Abstract: 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 layer Ω + δ by using the techniques of asymptotic expansion with scaling, which allows us to approximate the transmission problem by a boundary value problem doesn’t take into …account any more the thin layer Ω + δ , called approximate impedance problem; after that, we prove an error estimate between the solution of the transmission problem and the solution of the approximate impedance problem. Show more

Keywords: Couple stress elasticity with voids, porous micropolar layer, Dirichlet-to-Neumann operator, impedance operator, asymptotic expansion

DOI: 10.3233/ASY-231886

Citation: Asymptotic Analysis, vol. 137, no. 3-4, pp. 245-265, 2024

Authors: Zhang, Jiangwei | Xie, Zhe | Xie, Yongqin

Article Type: Research Article

Abstract: 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 parameter ν in M t is obtained. It’s remarkable that the nonlinearity f satisfies the polynomial growth of arbitrary order.

Keywords: Nonclassical diffusion equation, arbitrary polynomial growth, pullback attractor, memory, upper semi-continuity

DOI: 10.3233/ASY-231887

Citation: Asymptotic Analysis, vol. 137, no. 3-4, pp. 267-289, 2024

Authors: Khelifi, Hichem

Article Type: Research Article

Abstract: In this paper, we are interested in the existence and regularity of solutions for some anisotropic elliptic equations with Hardy potential and L m ( 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 the solutions, that is related to an anisotropic Hardy inequality.

Keywords: Anisotropic elliptic problems, existence and regularity, Hardy potential, irregular data, Hardy inequality

DOI: 10.3233/ASY-231889

Citation: Asymptotic Analysis, vol. 137, no. 3-4, pp. 291-303, 2024