Exponential decay for a strain gradient porous thermoelasticity with second sound

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Submitted: 2024-12-05; Published: 2024-12-05

This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

Abstract

In this paper, we consider a strain gradient porous elastic bar subjected to a thermal disturbance modelled by Cattaneo's law for heat conduction. We use the semigroup approach to prove the existence of a unique weak solution. Although the thermal dissipation induced by the second sound thermoelasticity is weaker than that caused by the classical heat conduction, we prove that the solution decays exponentially.