Uniform Decays in Nonlinear Thermoelastic Systems
The uniform stability of a nonlinear thermoelastic plate model is investigated, where the abstract nonlinearity here satisfies assumptions which allow the specification of the von Kármán nonlinearity, among other physically relevant examples. Linear analogs of this work were considered in  and . Even in the absence of inserted dissipative feedbacks on the boundary, this system is shown to be stable with exponential decay rates which are uniform with respect to the “finite energy” of the given initial data (uniform stability of a linear thermoelastic plate with added boundary dissipation was shown in , as was that of the analytic case in ). The proof of this result involves a multiplier method, but with the particular multiplier invoked being of a rather nonstandard (operator theoretic) nature. In addition, the “free” boundary conditions in place for the plate component give rise to higher order terms which pollute the decay estimates, and to deal with these a new result for boundary traces of the wave equation must be employed.
KeywordsExponential Stability Free Boundary Condition Boundary Trace Exponential Decay Rate Uniform Decay
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