PDE Geometric Analysis seminar
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.
Seminar Schedule Spring 2012
|Feb 6||Yao Yao (UCLA)||Kiselev|
|March 12||Xuan Hien Nguyen (Iowa State)||Angenent|
|March 19||Nestor Guillen (UCLA)||Feldman|
|March 26||Vlad Vicol (University of Chicago)||Kiselev|
|April 16||Jiahong Wu (Oklahoma)||Kiselev|
Yao Yao (UCLA)
Degenerate diffusion with nonlocal aggregation: behavior of solutions
The Patlak-Keller-Segel (PKS) equation models the collective motion of cells which are attracted by a self-emitted chemical substance. While the global well-posedness and finite-time blow up criteria are well known, the asymptotic behaviors of solutions are not completely clear. In this talk I will present some results on the asymptotic behavior of solutions when there is global existence. The key tools used in the paper are maximum-principle type arguments as well as estimates on mass concentration of solutions. This is a joint work with Inwon Kim.
Xuan Hien Nguyen (Iowa State)
Gluing constructions for solitons and self-shrinkers under mean curvature flow
In the 1990s, Kapouleas and Traizet constructed new examples of minimal surfaces by desingularizing the intersection of existing ones with Scherk surfaces. Using this idea, one can find new examples of self-translating solutions for the mean curvature flow asymptotic at infinity to a finite family of grim reaper cylinders in general position. Recently, it has been shown that it is possible to desingularize the intersection of a sphere and a plane to obtain a family of self-shrinkers under mean curvature flow. I will discuss the main steps and difficulties for these gluing constructions, as well as open problems.
Nestor Guillen (UCLA)
Vlad Vicol (University of Chicago)
Jiahong Wu (Oklahoma State)