Spatial behavior in dynamical thermoviscoelasticity backward in time for porous media

ABSTRACTIn this article we study the spatial behavior of solutions to the backward in time problem associated with the linear theory of thermoviscoelastic materials with voids. We consider an appropriate time-weighted volume measure associated with the final boundary value problem and then, in terms of such measure, we obtain a first-order partial differential inequality. Some spatial estimates of Saint-Venant type are established.