Fall 2014

Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact Yassine Boubendir.

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Date: November 21, 2014

Speaker: Margaret Beck
Department of Mathematics and Statistics,
Boston University

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Title: "Nonlinear Stability of Coherent Structures via Pointwise Estimates"

Abstract:

Coherent structures, for example traveling waves and periodic patterns, play a key role in determining the behavior of certain types of PDEs, such as reaction diffusion equations and viscous conservation laws. In particular, if they are stable, then they attract nearby initial data and thus qualitatively govern the local dynamics for large times. Determining the stability of coherent structures is often complicated by the presence of continuous spectrum for the associated linearized operator, as well as by details of the nonlinear terms in the PDE. In this talk, I will explain such difficulties in the context of patterns known as defects, and explain how they can be overcome using so-called pointwise estimates for the associated Green's function.