Asymptotic stability

Tuesday, November 1, 2016 - 9:00am - 9:50am
Eduard-Wilhelm Kirr (University of Illinois at Urbana-Champaign)
I will discuss classical and recent results regarding asymptotic stability of solitary waves i.e., localized solutions of nonlinear wave equations propagating without changing shape. Begining with the work of Soffer and Weinstein in the ’90 we know that, under certain assumptions, solutions starting close to a solitary wave shadow nearby solitary waves before collapsing on one. The mathematical analysis relies on using dispersive estimates for the linearized dynamics at a fixed (rather arbitrarily chosen) solitary wave to control the nonlinearity.
Thursday, June 28, 2012 - 11:00am - 11:50am
Joe Conlon (University of Michigan)
This talk is concerned with the stability and asymptotic stability at large time of solutions to a system of equations, which includes the Lifschitz-Slyozov-Wagner (LSW) system in the case when the initial data has compact support. The main result is a proof of weak global asymptotic stability for LSW like systems. Comparison to a quadratic model plays an important part in the proof of the main theorem when the initial data is critical. The quadratic model extends the linear model of Carr and Penrose. This is joint work with Barbara Niethammer.
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