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The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand.
Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
Authors: Carita, Graça | Zappale, Elvira
Article Type: Research Article
Abstract: An integral representation result is obtained for the relaxation of a class of energy functionals depending on two vector fields with different behaviors which appear in the context of thermochemical equilibria and are related to image decomposition models and directors theory in nonlinear elasticity.
Keywords: relaxation, convexity-quasiconvexity
DOI: 10.3233/ASY-161383
Citation: Asymptotic Analysis, vol. 100, no. 1-2, pp. 1-20, 2016
Authors: Lafontaine, David
Article Type: Research Article
Abstract: We show the H 1 scattering for a one dimensional nonlinear Schrödinger equation with a non-negative, repulsive potential V such that V , x V ∈ W 1 , 1 , and a mass-supercritical non-linearity. We follow the approach of concentration-compacity/rigidity first introduced by Kenig and Merle.
Keywords: nonlinear Schrödinger equation, scattering, potential perturbation
DOI: 10.3233/ASY-161384
Citation: Asymptotic Analysis, vol. 100, no. 1-2, pp. 21-39, 2016
Authors: Mustafa, Muhammad I.
Article Type: Research Article
Abstract: In this paper we consider a plate equation with internal feedback and viscoelastic damping localized on a part of the boundary. Without imposing restrictive assumptions on the time-dependent frictional damping, we establish an explicit and general decay rate result that allows a wider class of relaxation functions and generalizes previous results existing in the literature.
Keywords: plate equation, general decay, viscoelastic damping, relaxation function, frictional damping
DOI: 10.3233/ASY-161385
Citation: Asymptotic Analysis, vol. 100, no. 1-2, pp. 41-62, 2016
Authors: Ignatova, Mihaela | Kukavica, Igor
Article Type: Research Article
Abstract: We address the existence of solutions for the free-surface Euler equation with surface tension in a bounded domain. Considering the problem in Lagrangian variables we provide a priori estimates leading to existence of local solutions with the initial velocity in H 3.5 for which the trace on the free boundary belongs to H 3.5 .
Keywords: Euler equations, surface tension, free boundary
DOI: 10.3233/ASY-161386
Citation: Asymptotic Analysis, vol. 100, no. 1-2, pp. 63-86, 2016
Authors: Ammari, Habib | Giovangigli, Laure | Kwon, Hyeuknam | Seo, Jin-Keun | Wintz, Timothée
Article Type: Research Article
Abstract: In this paper, we present a simplified electrical model for tissue culture. We derive a mathematical structure for overall electrical properties of the culture and study their dependence on the frequency of the current. We introduce a method for recovering the microscopic properties of the cell culture from the spectral measurements of the effective conductivity. Numerical examples are provided to illustrate the performance of our approach.
Keywords: cell culture, conductivity properties, spectroscopic conductivity measurements, inverse homogenization
DOI: 10.3233/ASY-161387
Citation: Asymptotic Analysis, vol. 100, no. 1-2, pp. 87-109, 2016
Authors: Bardos, Claude | Hutridurga, Harsha
Article Type: Research Article
Abstract: This article is on the simultaneous diffusion approximation and homogenization of the linear Boltzmann equation when both the mean free path ε and the heterogeneity length scale η vanish. No periodicity assumption is made on the scattering coefficient of the background material. There is an assumption made on the heterogeneity length scale η that it scales as ε β for β ∈ ( 0 , ∞ ) . In one space dimension, we prove that the solutions to the kinetic model converge to the solutions of an effective diffusion …equation for any β ⩽ 2 in the ε → 0 limit. In any arbitrary phase space dimension, under a smallness assumption of a certain quotient involving the scattering coefficient in the H − 1 2 norm, we again prove that the solutions to the kinetic model converge to the solutions of an effective diffusion equation in the ε → 0 limit. Show more
Keywords: diffusion approximation, homogenization, moments method, velocity averaging lemma
DOI: 10.3233/ASY-161388
Citation: Asymptotic Analysis, vol. 100, no. 1-2, pp. 111-130, 2016
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