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On the spatial decay for the dynamical problem of thermo-microstretch elastic solids. (English) Zbl 1211.74077
Summary: This paper derives spatial decay bounds for a dynamical problem of thermo-microstretch elasticity defined on a semi-infinite cylindrical region. Previous results for isothermal elastodynamics and the parabolic heat equation lead us to suspect that the solution of the problem should tend to zero faster than a decaying exponential of the distance from the finite end of the cylinder. We prove that an energy expression is actually bounded above by a decaying exponential of a quadratic polynomial of the distance.

MSC:
74F05 Thermal effects in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
74G50 Saint-Venant’s principle
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