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On smooth solutions of the Cauchy problem in one-dimensional nonlinear thermoelasticity. (English) Zbl 0692.73005
An energy method is used to establish global existence and decay of classical solutions to the Cauchy problem with smooth and ‘small’ data in one-dimensional nonlinear thermoelasticity in which a thermoelastic body occupies the entire real line. The result is in agreement with that of B. D. Coleman and M. E. Gurtin [cf. Arch. Rational. Mech. Anal., 19, 266-298 (1965; Zbl 0244.73018)] who showed that in a one- dimensional nonlinear thermoelastic body only acceleration waves of ‘small’ initial amplitude reveal a decay behaviour.
The reviewer notes a number of misprints; e.g., in the estimates (4.29), (4.31) and (4.32) the function E(t) should be replaced by \(\xi\) (t).
Reviewer: J.Ignaczak

MSC:
74A15 Thermodynamics in solid mechanics
74F05 Thermal effects in solid mechanics
35B65 Smoothness and regularity of solutions to PDEs
74S30 Other numerical methods in solid mechanics (MSC2010)
74B20 Nonlinear elasticity
49J45 Methods involving semicontinuity and convergence; relaxation
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