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On the Cauchy problem in nonlinear 3-D-thermoelasticity. (English) Zbl 0701.73002
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 S. Klainerman and G. Ponce [Commun. Pure Appl. Math., 36, 133-141 (1983; Zbl 0509.35009)], F. John [ibid. 30, 421-446 (1977; Zbl 0404.73023)], S. Kawashima [Systems of a hyperbolic-parabolic type with applications to equations of magnetohydrodynamics, Thesis, Kyoto Univ. (1983)] and R. Leis [Initial boundary value problems in mathematical physics (1986; Zbl 0599.35001)].
Reviewer: J.Ignaczak

MSC:
74A15 Thermodynamics in solid mechanics
74B20 Nonlinear elasticity
35B65 Smoothness and regularity of solutions to PDEs
35M20 PDE of composite type (MSC2000)
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