  The aim of this paper is to study the spatial behaviour of the solutions to
the boundary-final value problems associated with the linear theory of elastic
materials with voids. More precisely the present study is devoted to porous
materials with a memory effect for the intrinsic equilibrated body forces. An
appropriate time-weighted volume measure is associated with the backward in
time thermoelastic processes.
  Then, a first-order partial differential inequality in terms of such measure
is established and further is shown how it implies the spatial exponential
decay of the thermoelastic process in question.
