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DTSTART;TZID=America/New_York:20181206T150000
DTEND;TZID=America/New_York:20181206T160000
DTSTAMP:20220520T202855
CREATED:20181128T173511Z
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UID:5014-1544108400-1544112000@math.unc.edu
SUMMARY:Perry Kleinhenz\, Northwestern University - Wunsch/PDE Mini-school
DESCRIPTION:View Full Schedule here \nTitle: Stabilization rates for the damped wave equation with Hölder regular damping \nAbstract: 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.
URL:https://math.unc.edu/event/perry-kleinhenz-northwestern-university-wunsch-pde-mini-school/
LOCATION:Phillips 383
CATEGORIES:Analysis & PDE Seminar,PDE Mini-school
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