Existence and uniqueness of solutions of thermo-poroelasticity

Abstract

We present results on the existence and uniqueness of a new formulation of wave propagation in linear thermo-poroelastic isotropic media in bounded domains under appropriate boundary and initial conditions. The linear theory of thermo-poroelasticity describes wave propagation in fluid-saturated poroelastic media including the temperature. In the model analyzed here, the constitutive equations in Biot's theory are modified by introducing coupling temperature terms, while the heat equation is generalized by including the coupling with the elastodynamic field and relaxation terms, the latter to model finite velocities. This analysis shows the existence of a unique solution, given in terms of displacements of the solid and fluid phases and temperature, and proves its regularity in the space and time variables.