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

Abstract

<p style='text-indent:20px;'>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.</p>