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

Catherine Lebiedzik | Zendy

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

Author(s) -

Catherine Lebiedzik

Publication year - 2020

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.

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