Stability and Convergence of Modal Approximations in Coupled Thermoelastic Systems: Theory and Simulation

TL;DR

This paper investigates the stability and convergence of modal approximations in coupled thermoelastic systems, combining spectral analysis and numerical simulations to understand decay rates and the influence of initial data regularity.

Contribution

It provides a comprehensive analysis of spectral properties and decay rates in thermoelastic systems, highlighting the impact of modal approximations on energy dissipation and stability.

Findings

Uniform polynomial decay rates are established under certain boundary conditions.

Regularity of initial data significantly affects observed decay rates.

Numerical experiments confirm theoretical predictions about energy dissipation.

Abstract

In this work, we review and analyze both the theoretical and numerical aspects of strongly and weakly coupled thermoelastic systems. By employing spectral analysis techniques and establishing uniform resolvent estimates, we derive uniform polynomial decay rates for the associated semigroups under a suitable class of boundary conditions. Particular attention is paid to the role of modal approximations in energy analysis. The theoretical results are complemented by numerical experiments that illustrate how the regularity of initial data, smooth versus nonsmooth, affects the observed decay rates, providing deeper insight into the interplay between spectral structure and energy dissipation.