Global Existence and Exponential Stability for a Nonlinear Thermoelastic Kirchhoff-Love Plate

TL;DR

This paper proves the global existence and exponential stability of solutions for a quasilinear thermoelastic Kirchhoff-Love plate model, using barrier techniques under small initial data assumptions.

Contribution

It is the first to establish global existence and exponential stability for a quasilinear non-parabolic thermoelastic Kirchhoff-Love plate in multiple dimensions.

Findings

Global existence of solutions proven under small initial data.

Exponential stability of solutions demonstrated.

First such result for this class of thermoelastic plates.

Abstract

We study an initial-boundary-value problem for a quasilinear thermoelastic plate of Kirchhoff \& Love-type with parabolic heat conduction due to Fourier, mechanically simply supported and held at the reference temperature on the boundary. For this problem, we show the short-time existence and uniqueness of classical solutions under appropriate regularity and compatibility assumptions on the data. Further, we use barrier techniques to prove the global existence and exponential stability of solutions under a smallness condition on the initial data. It is the first result of this kind established for a quasilinear non-parabolic thermoelastic Kirchhoff & Love plate in multiple dimensions.