Exponential stabilization for porous elastic system with one boundary dissipation

Abstract

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 $${\mathcal {A}}$$ 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.