  In the present study we consider the theory of thermoelastodynamics in the
case of materials with double porosity structure and microtemperature. This
study is devoted to the investigation of a backward in time problem associated
with double porous thermoelastic materials with microtemperature. In the first
part of the paper, in case of the bounded domains the impossibility of time
localization of solutions is obtained. This study is equivalent to the
uniqueness of solutions for the backward in time problem. In the second part of
the paper, a Phragmen-Lindelof alternative in the case of semi-infinite
cylinders is obtained.
