On the uniqueness and spatial behaviour of anti-plane shear deformations of swelling porous elastic soils backward in time

This paper is concerned with the backward in time problem in the theory of anti-plane shear deformations of swelling porous elastic soils in the case of fluid saturation and/or gas saturation. The formulation belongs to the theory of mixtures of porous elastic solids filled with fluid and/or gas. These problems propose some new mathematical difficulties. We prove the uniqueness of solutions of the backward in time problem of anti-plane shear deformations. We also study the spatial behaviour of solutions of this problem.