Exponential stability of an uncontrolled thermoelastic system with varying boundary conditions^*

^*A preliminary version of this work hasapproved in a special issue of Rendiconti De1l'lstituio Di Matematica Dell'Univcraiid Di Triesie, in honour or Pierre Crisvnal.

Abstract

We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary(uniform stability of a thermoelastic plate with added boundary dissipation was shown in [3], as was that of the analytic case where rotational forces are negleted in [9]); both the analytic and nonanalytic cases are treated here. The proof is constructive in the sense that we make use of a multiplier with respect to the coupled system involved so as to generate a fortiori the desired estimates; this multiplier is of an operator theoretic nature, as opposed to the more standard differential quantities used for such work. Moreover, the particular choice of multiplier becomes clear only after recasting the pde model into an associated abstract evolution equation. With this direct technique, we also obtain an exponential stability estimate pertaining to the limit case in which rotational inertia is neglected, and which leads to an associated analytic semigroup.

Keywords:

• Stability
• thermoelasticity
• well-posedness

^*A preliminary version of this work hasapproved in a special issue of Rendiconti De1l'lstituio Di Matematica Dell'Univcraiid Di Triesie, in honour or Pierre Crisvnal.

^†Department of mathematics, Texas. Tech university, Lubbock, Texas, USA

^‡Department of Applied mathematicsThornton Hall University of Virginia. Charlottesville, Virginia, USA.

^*A preliminary version of this work hasapproved in a special issue of Rendiconti De1l'lstituio Di Matematica Dell'Univcraiid Di Triesie, in honour or Pierre Crisvnal.

^†Department of mathematics, Texas. Tech university, Lubbock, Texas, USA

^‡Department of Applied mathematicsThornton Hall University of Virginia. Charlottesville, Virginia, USA.

Notes

^*A preliminary version of this work hasapproved in a special issue of Rendiconti De1l'lstituio Di Matematica Dell'Univcraiid Di Triesie, in honour or Pierre Crisvnal.

^†Department of mathematics, Texas. Tech university, Lubbock, Texas, USA

^‡Department of Applied mathematicsThornton Hall University of Virginia. Charlottesville, Virginia, USA.