Asymptotic Analysis - Volume 58, issue 4

Authors: Meirmanov, Anvarbek

Article Type: Research Article

Abstract: A linear system of differential equations describing a joint motion of a thermoelastic porous body with a sufficiently large Lamé's constants (absolutelty rigid body) and a thermofluid, occupying porous space, is considered. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for homogenization procedures as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic. As the results we derive Darcy's system of filtration or acoustic equations for thermofluid, depending on ratios between physical parameters. The proofs are based on Nguetseng's two-scale convergence method of homogenization in periodic structures.

Keywords: anisothermic Stokes and Lamé's equations, two-scale convergence, homogenization of periodic structures

DOI: 10.3233/ASY-2008-0881

Citation: Asymptotic Analysis, vol. 58, no. 4, pp. 191-209, 2008

Authors: Carles, Rémi | Masaki, Satoshi

Article Type: Research Article

Abstract: We justify WKB analysis for Hartree equation in space dimension at least three, in a régime which is supercritical as far as semiclassical analysis is concerned. The main technical remark is that the nonlinear Hartree term can be considered as a semilinear perturbation. This is in contrast with the case of the nonlinear Schrödinger equation with a local nonlinearity, where quasilinear analysis is needed to treat the nonlinearity.

Keywords: Hartree equation, WKB analysis, Zhidkov spaces, instability

DOI: 10.3233/ASY-2008-0882

Citation: Asymptotic Analysis, vol. 58, no. 4, pp. 211-227, 2008

Authors: Vasconcellos, Carlos F. | da Silva, Patricia N.

Article Type: Research Article

Abstract: We study the stabilization of global solutions of the linear Kawahara (K) equation in a bounded interval under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model. We also prove that the decay of solutions, in absence of damping, fails for some critical values of the length L and we define precisely this countable set. Finally, we include some remarks about nonlinear problem and we analyze the exact boundary control for linear Kawahara …system. Show more

DOI: 10.3233/ASY-2008-0895

Citation: Asymptotic Analysis, vol. 58, no. 4, pp. 229-252, 2008

Article Type: Other

Citation: Asymptotic Analysis, vol. 58, no. 4, pp. 253-253, 2008