Some properties of solutions in linear theory for semi-strongly elliptic porous elastic materials

This paper is concerned with the linear theory of elastodynamics for homogeneous, isotropic, porous elastic materials with memory effects for the intrinsic equilibrated body forces. We are able to relax the conditions on constitutive coefficients and to determine the wider class of materials for which the internal energy is positive semi-definite, when boundary conditions are homogeneous. We found the class of semi-strongly elliptic porous elastic materials. For this class of materials, the above conditions may be relaxed without loss of some well-posedness properties of the solutions. In particular, we obtain uniqueness of the solutions and we study the spatial behavior problem.