Maximal regularity and global existence of solutions to a quasilinear thermoelastic plate system

TL;DR

This paper proves the well-posedness and exponential decay of solutions for a quasilinear PDE system modeling nonlinear vibrations of a thermoelastic plate, ensuring maximal regularity and stability in bounded domains.

Contribution

It establishes maximal parabolic regularity and global existence results for nonlinear thermoelastic plate equations, which were previously unproven.

Findings

Solutions exist globally and are well-posed.

Strong solutions decay exponentially over time.

Maximal regularity results are achieved for the PDE system.

Abstract

We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in R^n. Well-posedness of solutions reconstructing maximal parabolic regularity in nonlinear thermoelastic plates is established. In addition, exponential decay rates for strong solutions are also shown.