Well-posedness and stability results for a swelling porous-heat system of second sound

Abstract

In this work, we consider a swelling porous-elastic system coupled with a heat system of second sound. We establish the existence of solutions then we prove an exponential decay result. Unlike the “purely” porous system, this result is obtained without the equal-speed requirement. We also perform some numerical tests to illustrate our theoretical findings.

Keywords:

• Exponential decay
• heat
• second sound
• swelling porous

AMS Subject Classifications:

• 93D20
• 34G10
• 35B40
• 35L90
• 45K05

Acknowledgments

The authors thank an anonymous referee for her or his valuable remarks and suggestions; and the University of Ahmed Draia, University of Sharjah and KFUPM for their support. The first author is partially supported by the DGRSDT of Algeria and the second author is sponsored by KFUPM, Grant No. SB201005.

Data availability

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

Short statement and significance of the work

In architectural and civil engineering, swelling soils are considered to be sources of problems and harms. To overcome such difficulty and stabilize building, roads and pavements, various damping mechanisms have been used.

In our work, we show that heat dissipation can be used to stabilize such porous systems. So, we consider a swelling porous-elastic system coupled with a heat system of second sound and show that the problem is well posed. In addition, we establish an exponential decay result without the equal speed condition requirement. We also perform some numerical tests to illustrate our theoretical findings.

Our result will give new contributions to the theory associated with asymptotic behaviors of swelling porous elastic soils.

Additional information

Funding

The first author is partially supported by the DGRSDT of Algeria and the second author is sponsored by KFUPM, Grant No. SB201005.