Exponential and Polynomial Decay Rates of a Porous Elastic System with Thermal Damping

Abstract

This paper concerns a linear porous thermoelastic system, where the heat conduction is given by Cattaneo’s law. By using the theory of the semigroup of the linear operator, the well-posedness is proven. By constructing some suitable multipliers, we establish exponential and polynomial decay rates of the system depending on a stability number $\pi$ . In addition, we remove the assumption that the constant $b$ is positive in the previous works, which extends some existing results in the literature.