Exponential stabilization for porous elastic system with one boundary dissipation

In this paper, we consider the one-dimensional porous elastic system with mixed dissipation term at the point x=0 acting only on the volumetric fraction of the system. We prove that the operator 𝒜 associated with the problem is an infinitesimal generator of a C_0 –semigroup of contractions and we prove the exponential stability if an important restriction is imposed on the constitutive coefficients.