The author has supplied the accompanying file:
"Erratum to: Decay Rates to Equilibrium for Nonlinear Plate Equations with Degenerate, Geometrically-Constrained Damping (vol 68, pg 361, 2013)." This erratum was also published in the December 2014 issue of the journal Applied Mathematics and Optimization, 70(3), 565-566. doi: 10.1007/s00245-014-9275-z
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://link.springer.com/journal/245.
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 , 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.
Geredeli, P. G., & Webster, J. T. (2013). Decay rates to equilibrium for nonlinear plate equations with degenerate, geometrically-constrained damping. Applied Mathematics and Optimization, 68(3), 361-390. doi:10.1007/s00245-013-9210-8