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Rapidly decreasing behaviour of solutions in nonlinear 3-D- thermoelasticity. (English) Zbl 0709.73006

This paper is concerned with the asymptotic behaviour with respect to the space variable (i.e. when \(| x| \to \infty)\) of the solution of a fully nonlinear system in three-dimensional thermoelasticity. Two situations, for which known existence and uniqueness results are recalled, are examined: local existence in time and global existence in time for small enough data. Under adequate assumptions on the data the author derives a few estimates on the space and time derivatives of the solution in weighted Sobolev spaces. The techniques relie on known energy estimates for such a system and on some new a priori estimates (derived through the use of “weighted test functions”). Few extensions concerning exterior problems are mentioned.
Reviewer: D.Blanchard

MSC:

74A15 Thermodynamics in solid mechanics
74B20 Nonlinear elasticity
35B40 Asymptotic behavior of solutions to PDEs
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