Maximal regularity and global existence of solutions  to a quasilinear  thermoelastic plate  system

Irena Lasiecka; Mathias Wilke

doi:10.3934/dcds.2013.33.5189

Article Contents

2013, Volume 33, Issue 11&12: 5189-5202. Doi: 10.3934/dcds.2013.33.5189

This issue Previous Article Coagulation and fragmentation processes with evolving size and shape profiles: A semigroup approach Next Article Stability estimates for semigroups on Banach spaces

Maximal regularity and global existence of solutions to a quasilinear thermoelastic plate system

Irena Lasiecka^1, and
Mathias Wilke^2,

1.
Department of Mathematics, University of Virginia, Charlottesville, VA 22903
2.
Institut für Mathematik, Martin-Luther Universität Halle-Wittenberg, 06099 Halle

Received: October 31, 2011

Revised: September 30, 2012

Published: October 2013

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Abstract

We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in $\mathbb{R}^n$. Global Well-posedness of solutions is shown by applying the theory of maximal parabolic regularity of type $L_p$. In addition, we prove exponential decay rates for strong solutions and their derivatives.

Keywords:

Quasilinear thermoelastic plates,
existence and uniqueness of strong solutions,
maximal regularity,
exponential decay.

Mathematics Subject Classification: Primary: 74F05; Secondary: 35B30, 35B40, 74H40.

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