Asymptotic behavior of reflection of discontinuities in thermoelasticity with second sound in one space variable
type: Item
instance of: scholarly article
title: Asymptotic behavior of reflection of discontinuities in thermoelasticity with second sound in one space variable
zbMATH Open document ID: 1237.74023
author: Zheng Li
author: Yaguang Wang
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2011-09-13T00:00:00Z
review text: The authors consider an initial boundary value problem for the semilinear thermoelastic system with second sound in \(\{t, x > 0\}\). By using a technique introduced in [\textit{R. Racke}, Lectures on nonlinear evolution equations. Initial value problems. Aspects of Mathematics. 19. Braunschweig etc.: Vieweg (1992; Zbl 0811.35002)], they prove the existence of a local solution and the global existence of a small solution to the initial boundary value problem mentioned above under certain conditions on the growth rate of the nonlinear functions \((f,g)\) on the right-side of the mixed problem with respect to their arguments, provided that the initial data are smooth and satisfy some compatibility conditions. The attention of the authors is directed to the behavior of discontinuities of the solutions under the hypothesis that the problem has a solution in a time interval. In fact, the authors study the reflection of discontinuous waves on physical boundaries in thermoelasticity and to investigate the influence of physical coefficients of linearized thermoelastic operator on the asymptotic behavior of singularities.
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74H40
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35Q74
zbMATH DE Number: 5947384
zbMATH Keywords: hyperbolic thermoelasticity
zbMATH Keywords: semilinear
zbMATH Keywords: discontinuities
zbMATH Keywords: reflection
zbMATH Keywords: asymptotic behavior
reviewed by: Marin I. Marin
MaRDI profile type: Publication
full work available at URL: s00033-010-0069-0
OpenAlex ID: W2085862424
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DOI: 10.1007/S00033-010-0069-0
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description: scientific article; zbMATH DE number 5947384