Open AccessUniform stability in a vectorial full Von Kármán thermoelastic system with solenoidal dissipation and free boundary conditions
Author(s) -
Catherine Lebiedzik
Publication year - 2021
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2020092
Subject(s) - thermoelastic damping , dissipation , solenoidal vector field , semigroup , physics , boundary (topology) , mathematical analysis , trace (psycholinguistics) , displacement (psychology) , plane (geometry) , mathematics , boundary value problem , mathematical physics , geometry , thermodynamics , mechanics , vector field , thermal , psychology , linguistics , philosophy , psychotherapist
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.