Energy decay analysis for Porous elastic system with microtemperature : A second spectrum approach

TL;DR

This paper investigates the energy decay and stability of a porous elastic system with microtemperature using a second spectrum approach, providing theoretical proofs, numerical validation, and error estimates.

Contribution

It introduces a novel analysis of energy decay in porous elastic systems with microtemperature via second spectrum methods, including stability proofs and finite element approximations.

Findings

Global existence and uniqueness of solutions proven.

Exponential stability without equal wave speed assumption.

Finite element method accurately captures energy decay.

Abstract

In this work, we analyze porous elastic system with microtemperature from second spectrum viewpoint. Indeed, by using the classical Faedo-Galerkin method combined with the a priori estimates, we prove the existence and uniqueness of a global solution of this problem. Then we prove that this solution is exponentially stable without assuming the condition of equal wave speeds. Then, we introduce a finite element approximation and we prove that the associated discrete energy decays. Finally, we obtain some a priori error estimates assuming additional regularity on the solution and we present some numerical results which demonstrate the accuracy of the approximation and the behaviour of the solution