On the porous-elastic system with Kelvin-Voigt damping

In this article we are considering the one-dimensional equations of a homogeneous and isotropic porous elastic solid with Kelvin-Voigt damping. We prove that the semigroup associated with the system (1.3) with Dirichlet-Dirichlet boundary conditions or Dirichlet-Neumann boundary conditions is analytic and consequently exponentially stable. On the other hand, we prove that the system (1.3) with Dirichlet-Neumann boundary conditions has lack of exponential decay and it decays as 1/root t for the case gamma(1) > 0, gamma(2) = 0 or gamma(1) = 0, gamma(2) > 0. Moreover, we prove that this rate is optimal. We apply the main results for the Timoshenko model. (C) 2016 Published by Elsevier Inc.