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Stabilization of swelling porous elastic soils with fluid saturation and delay time terms

In this article, we consider the swelling problem in porous elastic soils with fluid saturation. We study the well-posedness of the problem based on the semigroup theory, show that the energy associated with the system is dissipative, and establish the stability of the system in the exponential way. To guarantee the stability of the systems, we consider both viscous damping and the time delay term acting on the first equation of the system.