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Existence and Exponential Decay of Solutions to a Quasilinear Thermoelastic Plate System

  • Irena LasieckaEmail author
  • Sara Maad
  • Amol Sasane
Article

Abstract.

We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in \(\mathbb{R}^n\), 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].

Mathematics Subject Classification (2000).

Primary 74F05 Secondary 35B30, 35B40, 74H40 

Keywords.

Quasilinear thermoelastic plates existence of weak solutions uniform decays of finite energy solutions 

Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA
  2. 2.Department of MathematicsStockholm UniversityStockholmSweden
  3. 3.Department of MathematicsLondon School of EconomicsLondonUnited Kingdom

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