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Analysis Seminar – Michael Dabkowski (Lawrence Technological University)

September 22, 2017 @ 3:30 pm - 4:30 pm

Title: Global Stability of a Class of Nonlinear PDE with a Nonlocal Term

Abstract:

We will establish global asymptotic stability results for a class of non-linear PDE which arise in approximations of models of particle coarsening. These PDE must satisfy a conservation of mass constraint which induces a nonlocal term into the equation. Our method of proof makes use of the tempering of oscillations on large scales to overcome the lack of a Lyapounov function. The stability of the PDE is equivalent to stability for a differential delay equation. Using ideas from a classical result of Yorke, we prove the stability of the delay equation by certain maximal properties which are established by methods of optimal control.

Details

Date:
September 22, 2017
Time:
3:30 pm - 4:30 pm
Event Categories:
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Venue

227 Gordon Palmer Hall
505 Hackberry Lane
Tuscaloosa, AL 35487 United States
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