Uniform stability in a vectorial full Von Kármán thermoelastic system with solenoidal dissipation and free boundary conditions

Catherine Lebiedzik

doi:10.3934/eect.2020092

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2021, Volume 10, Issue 4: 767-796. Doi: 10.3934/eect.2020092

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Uniform stability in a vectorial full Von Kármán thermoelastic system with solenoidal dissipation and free boundary conditions

Catherine Lebiedzik

Wayne State University, Department of Mathematics, Detroit, MI 48201 USA

Received: February 2020

Revised: August 2020

Early access: September 2020

Published: December 2021

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Abstract

We will consider the full von Kármán thermoelastic system with free boundary conditions and dissipation imposed only on the in-plane displacement. It will be shown that the corresponding solutions are exponentially stable, though there is no mechanical dissipation on the vertical displacements. The main tools used are: (i) partial analyticity of the linearized semigroup and (ii) trace estimates which exploit the hidden regularity harvested from partial analyticity.

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Mathematics Subject Classification: Primary:35B35, 35M30, 74B20, 74F05, 74K20;Secondary:35A01, 35A02.

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