# Margaret Beck : Nonlinear stability of time-periodic viscous shocks

In order to understand the nonlinear stability of many types of time-periodic traveling waves on unbounded domains, one must overcome two main difficulties: the presence of zero eigenvalues that are embedded in the continuous spectrum and the time-periodicity of the associated linear operator. I will outline these issues and show how they can be overcome in the context of time-periodic Lax shocks in systems of viscous conservation laws. The method involves the development of a contour integral representation of the linear evolution, similar to that of a strongly continuous semigroup, and detailed pointwise estimates on the resultant Greens function, which are sufficient for proving nonlinear stability under the necessary assumption of spectral stability.

**Category**: Applied Math and Analysis**Duration**: 01:14:49**Date**: December 8, 2008 at 4:25 PM**Views**: 141-
**Tags:**seminar, Applied Math And Analysis Seminar

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