In this chapter we study well-posedness and regularity issues associated with thermoelastic plates. The PDE model of thermoelasticity consists of coupled second-order (plate) and first-order (heat) equations. For this reason, treatment of thermoelastic models does not follow from the corresponding treatment of abstract second-order equations. A new functional framework needs to be developed.
In this chapter we undertake a study of solutions associated with von Karman evolution equations subject to thermal dissipation. We consider models with and without the rotational inertia terms.
KeywordsStrong Solution Exponential Stability Continuous Semigroup Contraction Semigroup Resolvent Estimate
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- 61.I. Chueshov, Introduction to the Theory of Infinite-Dimensional Dissipative Systems, Acta, Kharkov, 1999, in Russian; English translation: Acta, Kharkov, 2002; see also http://www.emis.de/monographs/Chueshov/
- 159.T. Kato, Perturbation Theory of Linear Operators, Springer, New York, 1966.Google Scholar
- 178.J. Lagnese and J.L. Lions Modeling, Analysis and Control of Thin Plates, Masson, Paris, 1988.Google Scholar
- 216.I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations, Cambridge University Press, Cambridge, 2000.Google Scholar
- 241.A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1986.Google Scholar
- 242.M. Potomkin, Asymptotic behaviour of solutions to nonlinear problem in thermoelasticity of plates, Rep. Nat. Acad. Sci. Ukraine, 2 (2009), 26–31, in Russian.Google Scholar