On the asymptotic spatial behaviour in the theory of mixtures of thermoelastic solids

This paper is concerned with the study of asymptotic spatial behaviour of solutions in a mixture consisting of two thermoelastic solids. A second-order differential inequality for an adequate volumetric measure and the maximum principle for solutions of the one-dimensional heat equation are used to establish a spatial decay estimate of solutions in an unbounded body occupied by the mixture. For a fixed time, the result in question proves that the mechanical and thermal effects are controlled by an exponential decay estimate in terms of the square of the distance from the support of the external given data. The decay constant depends only on the thermal constitutive coefficients of the mixture.