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April 10, 2019 | 1:00 p.m. - 2:00 p.m.
Category: Seminar
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free
Speaker: Alaa Haj Ali (WSU)
 
Title: Symmetry and Approximate Symmetry of a Nonlinear Elliptic Problem over a Ring
 
Abstract: 

A singularly perturbed free boundary problem arising from a real problem associated with a Radiographic Integrated Test Stand concerns a solution of the equation $Delta u = f(u)$ in a domain subject to constant boundary data, where the function f in general is not monotone. When the domain is a perfect ring, we incorporate a new idea of radial correction into the classical moving plane method to prove the radial symmetry of a solution. When the domain is slightly shifted from a ring, we establish the stability of the solution by showing the approximate radial symmetry of the free boundary and the solution. For this purpose, we complete the proof via an evolutionary point of view, as an elliptic comparison principle is false, nevertheless a parabolic one holds.

For more information about this event, please contact Department of Mathematics at 3135772479 or math@wayne.edu.