Abstract
In this work, we derive stability properties for a nonlinear thermoelastic plate system in which the higher order “free” boundary conditions are enforced on the displacement of the plate. The class of nonlinearities under consideration here include those seen in classical models in mechanics; such as von Kármán systems, the quasilinear Berger’s equation which models extensible plates, and Euler-Bernoulli semilinear plates. This paper focuses on the case that rotational inertia is unaccounted for in the model, which corresponds to the absence of the parameter γ (i.e., γ = 0). In this case, we show that for initial data in the basic space of well-posedness, solutions of the PDE system decay to zero uniformly as time gets large. In our proof of uniform decay for γ = 0, absolutely critical use is made of the recently discovered fact that the linearization of the thermoelastic model generates an analytic semigroup.
Research supported in part by the National Science Foundation Grant No. DMS-9710981.
Research supported in part by the National Science Foundation Grant No. DMS-9504822, and by the Army Research Office Grant DAAH04-96-1-0059.
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Avalos, G., Lasiecka, I., Triggiani, R. (1999). Uniform Stability of Nonlinear Thermoelastic Plates with Free Boundary Conditions. In: Hoffmann, KH., Leugering, G., Tröltzsch, F., Caesar, S. (eds) Optimal Control of Partial Differential Equations. ISNM International Series of Numerical Mathematics, vol 133. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8691-8_2
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