On the Cauchy problem in nonlinear 3-D-thermoelasticity
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)].
nonlinear three- dimensional thermoelasticity
scientific article; zbMATH DE number 4149632