Resumen de Theoretical aspects of wave propagation for Biot's consolidation problem

Hélène Barucq , Monique Madaune-Tort , P. Saint-Macary

• We consider a coupled system of mixed hyperbolic-parabolic type which describes the Biot consolidation model in poro-elasticity as well as a coupled quasi-static problem in thermoelasticity. In this work, we intend to develop the existence-uniqueness theory for the multi-dimensional systems in the linear case using classical functional arguments in the Sobolev background. For the consolidation model, our approach involves Galerkin approximations to establish the existence of a solution to the problem while we prove that the thermo-elastic and the quasi-static systems are limit cases of the consolidation model. The treatment of the uniqueness is based on an energy inequality even if, in the quasi-static system, it requires some adjustments because of a lack of regularity.