# Asymptotic profiles of solutions for regularity-loss type generalized thermoelastic plate equations and their applications

## TL;DR

This paper analyzes the decay behavior and asymptotic profiles of solutions to generalized thermoelastic plate equations with Fourier heat conduction, examining the effects of structural damping and providing applications to related equations.

## Contribution

It introduces a decay threshold for regularity-loss in thermoelastic equations and characterizes solution profiles using Fourier and WKB analysis, including the impact of structural damping.

## Key findings

- Regularity-loss decay properties are characterized with a threshold.
- Structural damping destroys the regularity-loss structure.
- Asymptotic profiles are explicitly derived using Fourier analysis.

## Abstract

In this paper, we consider generalized thermoelastic plate equations with Fourier's law of heat conduction. By introducing a threshold for decay properties of regularity-loss, we investigate decay estimates of solutions with/without regularity-loss in a framework of weighted $L^1$ spaces. Furthermore, asymptotic profiles of solutions are obtained by using representations of solutions in the Fourier space, which are derived by employing WKB analysis. Next, we study generalized thermoelastic plate equations with additional structural damping, and analysis the influence of structural damping on decay properties and asymptotic profiles of solutions. We find that the regularity-loss structure is destroyed by structural damping. Finally, we give some applications of our results on thermoelastic plate equations and damped Moore-Gibson-Thompson equation.