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arXiv · 2307.04697

On the time behavior of a porous thermoelastic system with only thermal dissipation given by Gurtin-Pipkin law

Afaf Ahmima·Abdelfeteh Fareh
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Abstract

In the present paper we consider a porous thermoelastic system with only one dissipative mechanism generated by the heat conductivity modelled by the Gurtin-Pipkin thermal law. By the use of a semigroup approach and the Lumer-Phillips theorem we prove the existence of a unique solution. We introduce a stability number $\chi_g$ depends on the coefficients of the system, and establish an exponential stability result provided that $\chi_g=0$. Otherwise, if $\chi_g\ne 0$, we prove the lack of exponential decay. Our result improves and generalizes the previous results in the literature obtained for Fourier's and Cattaneo's laws of thermal conductivity.

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Afaf Ahmima, Abdelfeteh Fareh. 2023-07-10. On the time behavior of a porous thermoelastic system with only thermal dissipation given by Gurtin-Pipkin law. https://arxiv.org/abs/2307.04697

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