Exponential stability for one-dimensional problem of swelling porous elastic soils with fluid saturation

This paper concerns the one-dimensional linear theory of swelling porous elastic soils in the case of fluid saturation. The formulation belongs to the theory of mixtures for porous elastic solids filled with fluid. It proposes some new mathematical difficulties. We prove the exponential stability for the initial-boundary value problem determined by the homogeneous Dirichlet boundary conditions.