Anti-plane shear deformations of swelling porous elastic soils

This paper is concerned with the theory of anti-plane shear deformations of swelling porous elastic soils in the case of fluid saturation or gas saturation. The formulation belongs to the theory of mixtures for porous elastic solids filled with fluid or gas. These problems propose some new mathematical difficulties. We prove the exponential decay of solutions, a uniqueness result and the spatial decay of solutions (in the dynamical and the quasi-static cases). Some remarks are presented in the last section.