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

Abstract

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.

Keywords:

• Exponential stability
• Lord-Shulman
• swelling porous
• thermoelasticity
• well-posedness

AMS Subject Classifications:

• 35A01
• 93D23
• 74F05

Acknowledgement

The first three authors appreciate the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia, for funding this research work through institutional fund projects under the project no. IFP-A-2022-2-1-02.

Disclosure statement

The author declare no potential conflict of interests.

Data availability

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Additional information

Funding

This research work was funded by the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia, under the project IFP-A-2022-2-1-02.