On the impact of boundary conditions on weakly coupled thermoelastic wave model

TL;DR

This paper investigates how boundary conditions influence the long-term behavior of solutions in a thermoelastic wave model, showing that they do not affect asymptotic behavior but can alter decay rates.

Contribution

It proves well-posedness and analyzes the decay rates of energy under various boundary conditions in a thermoelastic wave system.

Findings

Boundary conditions do not affect asymptotic behavior.

Energy decays polynomially, not exponentially, under certain boundary conditions.

Global well-posedness is established under regularity assumptions.

Abstract

The purpose of this paper is to demonstrate how different types of boundary conditions do not impact the asymptotic behaviour of the solutions of thermoelastic wave model. For an initial-boundary value problem associated with this system, we prove a global well-posedness result in a certain topology under appropriate regularity conditions on the data. Further, we show that under particular classes of boundary conditions, the energy associated to the system decays polynomially to zero and not exponentially.