On the spatial behaviour in dynamics of porous elastic mixtures

Abstract

In this paper we study the spatial and temporal behaviour of the dynamic processes in porous elastic mixtures. For the spatial behaviour we use the time-weighted surface power function method in order to obtain a more precisely determination of the domain of influence and we establish spatial decay estimates of Saint-Venant type with time-independent decay rate for the inside of the domain of influence. For the asymptotic temporal behaviour we use the Cesaro means associated with the kinetic and strain energies and establish the asymptotic equipartition of the total energy. A uniqueness theorem is proved for finite and infinite bodies and we note that it is free of any kind of a priori assumptions of the solutions at infinity.