On the existence and exponential decay rate of swelling porous thermoelastic system of Lord-Shulman type

The article establishes the well-posedness and exponential decay rate results for a swelling porous system coupled with Lord-Shulman thermoelastic theory. The well-posedness result is established by exploiting the Lumer-Phillips corollary in conjunction with the Hille-Yoside theorem. The stabilization result is achieved using the energy/multiplier method without imposing the typical equal wave speeds or stability number phenomenon. Furthermore, we extend our results to a thermoelastic wave system influenced by the Lord-Shulman theory and demonstrate that the exponential stability result remains valid. Finally, numerical computations are conducted to validate the theoretical analysis.