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Perry Kleinhenz, Northwestern University – Wunsch/PDE Mini-school

December 6, 2018 @ 3:00 pm - 4:00 pm

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Title: Stabilization rates for the damped wave equation with Hölder regular damping

Abstract: We study the decay rate of the energy of solutions to the damped wave equation in a setup where the geometric control condition is violated. In particular we consider the case of a torus where the damping is $0$ on a strip and vanishes like a polynomial $x^{\beta}$. We prove that the semigroup is stable at rate at least as fast as $1/t^{(beta+2)/(\beta+4)}$ and sketch a proof that the semigroup decays no faster than $1/t^{(\beta+2)/(\beta+3)}$. These results establish an explicit relation between the rate of vanishing of the damping and rate of decay of solutions.


December 6, 2018
3:00 pm - 4:00 pm
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Phillips 383