Backward Uniqueness in Linear Thermoelasticity with Time and Space Variable Coefficients
Backward uniqueness for thermoelastic plates and thermoelastic waves with time- and space-dependent coefficients is established. While this result has been proved recently, in the case of time-independent coefficients, it is new for the case of time-dependent coefficients. The proof relies on a combination of energy and Carleman’s estimates, hence it is very different from the one given in [LRT], which is based on complex analysis methods. These latter methods are not applicable to nonlinear models and to models with time-dependent coefficients. Our results have consequences for several nonlinear models of thermoelasticity.
KeywordsEnergy Estimate Lumer Volume Homogeneous Dirichlet Boundary Condition Carleman Estimate Plate Equation
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