On well-posedness and exponential decay of swelling porous thermoelastic media with second sound

Abstract

This work focuses on the well-posedness and exponential stability results of a swelling porous thermoelastic system with heat flux given by Maxwell-Cattaneo's law. Precisely, using the well-known Lumer-Phillips theorem, we establish the well-posedness result of the system. Furthermore, using the multiplier method, we prove that the system is exponential stable irrespective of any stability number or equality of wave propagation. This result is unique and unexpected, especially when compared to similar problems like Timoshenko, Bresse, and thermoelasticity with second sound. In each of the systems mentioned above, a stability number is necessary for the exponential stability of the systems. Undoubtedly, our coupling and the result give new contributions to the asymptotic behaviors of swelling porous thermoelastic soils.