Approximation and Homogenization of Thermoelastic wave model

TL;DR

This paper investigates the approximation and homogenization of thermoelastic wave models with rapidly varying coefficients, using advanced mathematical techniques and numerical experiments to analyze spectral behavior and energy decay.

Contribution

It introduces a homogenization framework for weakly coupled thermoelastic waves and compares decay behaviors of different models through numerical analysis.

Findings

Homogenized semigroup obtained via Trotter Kato theorem.

Spectral behaviors differ between exponential and polynomial decay models.

Data smoothness affects energy decay rates.

Abstract

This paper deals with the approximation and homogenization of thermoelastic wave model. First, we study the homogenization problem of a weakly coupled thermoelastic wave model with rapidly varying coefficients, using a semigroup approach, two-scale convergence method and some variational techniques. We show that the limit semigroup can be obtained by using a weak version of the Trotter Kato convergence Theorem. Secondly, we consider the approximation of two thermoelastic wave model, one with exponential decay and the other one with polynomial decay. the numerical experiments indicate that the two discrete systems show different behavior of the spectra. Moreover, their discrete energies inherit the same behavior of the continuous ones. Finally we show numerically how the smoothness of data can impact the rate of decay of the energy associated the weakly coupled thermoelastic wave model.