Solutions for the unsteady motion of porous elastic solids within the context of an implicit constitutive theory

In this work we investigate well-posedness for the partial differential equation stemming from the balance of linear momentum for an implicit constitutive relation that can describe the response of porous elastic solids whose material moduli depend on the density. We study heteroclinic travelling waves and obtain closed form analytic solutions for the resulting ordinary differential equation. Finally, we consider some special solutions for the partial differential equation and solve the resulting equations numerically.