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Existence and exponential decay of solutions to a quasilinear thermoelastic plate system

Lasiecka, Irena, Maad, Sara and Sasane, Amol J. (2008) Existence and exponential decay of solutions to a quasilinear thermoelastic plate system. Nonlinear Differential Equations and Applications Nodea, 15 (6). pp. 689-715. ISSN 1021-9722

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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 Rn, n ≤ 3. Existence of finite energy solutions describing the dynamics of a nonlinear thermoelastic plate is established. In addition asymptotic long time behavior of weak solutions is discussed. It is shown that finite energy solutions decay exponentially to zero with the rate depending only on the (finite energy) size of initial conditions. The proofs are based on methods of weak compactness along with nonlocal partial differential operator multipliers which supply the sought after “recovery” inequalities. Regularity of solutions is also discussed by exploiting the underlying analyticity of the linearized semigroup along with a related maximal parabolic regularity [1, 16, 44].

Item Type: Article
Official URL: http://www.springer.com/birkhauser/mathematics/jou...
Additional Information: © 2008 Springer Birkhaeuser Verlag AG
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 27 Jul 2011 15:17
URL: http://eprints.lse.ac.uk/37627/

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