Generation of semigroups for the thermoelastic plate equation with free boundary conditions

TL;DR

This paper proves that the linear thermoelastic plate equations with free boundary conditions generate analytic semigroups in various domains, ensuring well-posedness and stability in $L^p$-spaces.

Contribution

It establishes the generation of analytic semigroups and maximal regularity for thermoelastic plate equations with free boundary conditions in diverse domains.

Findings

Operator generates an analytic semigroup in $L^p$-spaces for all $p ext{ in }(1, olinebreak ext{infinity})$

Maximal $L^q$-$L^p$-regularity holds on finite time intervals

Exponential stability achieved on bounded $C^4$-domains

Abstract

We consider the linear thermoelastic plate equations with free boundary conditions in uniform $C^4$-domains, which includes the half-space, bounded and exterior domains. We show that the corresponding operator generates an analytic semigroup in $L^p$-spaces for all $p\in(1,\infty)$ and has maximal $L^q$-$L^p$-regularity on finite time intervals. On bounded $C^4$-domains, we obtain exponential stability.