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Dalhousie-AARMS AAMP Seminar: Perry Kleinhenz (Michigan State University)

October 29, 2021 @ 4:00 pm - 5:00 pm

Title: Stabilization rates for the damped wave equation with polynomial and oscillatory damping

Abstract: In this talk I will discuss energy decay of solutions of the Damped wave equation. After giving an overview of classical results I’ll focus on the torus with damping that does not satisfy the geometric control condition. In this setup properties of the damping at the boundary of its support determine the decay rate, however a general sharp rate is not known.

I will discuss damping which is $0$ on a strip and vanishes either like a polynomial $x^b$ or an oscillating exponential $e^{-1/x} sin^2(1/x)$. Polynomial damping produces decay of the semigroup at exactly $t^{-(b+2)/(b+3)}$, while oscillating damping produces decay at least as fast as $t^{-4/5+\delta}$ for any $\delta>0$. I will explain how these model cases are proved and how they direct further study of the general sharp rate.


The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom.  If you would like to attend, please email the organizers for connection details.


October 29, 2021
4:00 pm - 5:00 pm
Event Category:


Zoom seminar


Suresh Eswarathasan