WebsterJustinMathematicsErratumTo:DecayRatesEquilibrium.pdf

Citeable URL: https://ir.library.oregonstate.edu/concern/articles/gq67jw85z

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Attribute Name	Values
Creator	Geredeli, Pelin G. Webster, Justin T.
Abstract	We analyze the convergence to equilibrium of solutions to the nonlinear Berger plate evolution equation in the presence of localized interior damping (also referred to as geometrically constrained damping). Utilizing the results in [24], we have that any trajectory converges to the set of stationary points N. Employing standard assumptions from the theory of nonlinear unstable dynamics on the set N, we obtain the rate of convergence to an equilibrium. The critical issue in the proof of convergence to equilibria is a unique continuation property (which we prove for the Berger equation) that provides a gradient structure for the dynamics. We also consider the more involved von Karman evolution, and show that the same results hold assuming a unique continuation property for solutions, which is presently a challenging open problem. Keywords: attractors, convergence to equilibrium, geometrically constrained damping, nonlinear plate equations, unique continuation Keywords: attractors, convergence to equilibrium, geometrically constrained damping, nonlinear plate equations, unique continuation
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