A general stability result for swelling porous elastic media with nonlinear damping

Abstract

We consider a swelling porous-elastic system with a single nonlinear damping in the elastic equation. Recently, Ramos et al. [Stability results for elastic porous media swelling with nonlinear damping. J Math Phys. 2020;61(10):101505.] considered the same system and established a general decay result provided that the wave speeds of the system are equal. In this paper, we obtain the general decay result without imposing a condition on the wave speeds of the system. This is a striking and unexpected result compared to Timoshenko system, porous systems, and Laminated beams system with similar damping. We also perform some numerical tests to illustrate our theoretical results.

Keywords:

• Swelling porous problem
• nonlinear damping
• general decay

AMS Subject Classifications::

• 93D20
• 35B40

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

T. Apalara has been supported by University Hafr Al-Batin [grant number G-106-2020]. A. Soufyane has been supported by University of Sharjah [grant number 1802144069].