On the Cauchy problem in nonlinear 3-D-thermoelasticity
type: Item
instance of: scholarly article
title: On the Cauchy problem in nonlinear 3-D-thermoelasticity
zbMATH Open document ID: 0701.73002
DOI: 10.1007/BF02570763
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174154
review text: The author shows that the Cauchy problem in a nonlinear three-dimensional thermoelasticity possesses a global smooth solution if the data are ``small'' and ``smooth'', and the material functions reveal a polynomial behaviour in a neighbourhood of homogeneous isotropic thermoelastic reference state. The proof is based upon the ideas of \textit{S. Klainerman} and \textit{G. Ponce} [Commun. Pure Appl. Math., 36, 133-141 (1983; Zbl 0509.35009)], \textit{F. John} [ibid. 30, 421-446 (1977; Zbl 0404.73023)], \textit{S. Kawashima} [Systems of a hyperbolic-parabolic type with applications to equations of magnetohydrodynamics, Thesis, Kyoto Univ. (1983)] and \textit{R. Leis} [Initial boundary value problems in mathematical physics (1986; Zbl 0599.35001)].
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35M20
zbMATH DE Number: 4149632
zbMATH Keywords: existence theorems
zbMATH Keywords: hyperbolic-parabolic coupled system
zbMATH Keywords: nonlinear three- dimensional thermoelasticity
zbMATH Keywords: global smooth solution
author: Reinhard Racke
reviewed by: Józef Ignaczak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4149632