On the spatial decay for the dynamical problem of thermo-microstretch elastic solids

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.