# Jim Nolen : On the great effect of small noise

This talk will include some PDE, some probability, and some asymptotic analysis. The FKPP equation is a nonlinear partial differential equation that admits traveling wave solutions. It has been used as a simple model for many phenomena involving a stable state invading an unstable state (for example, an advantageous gene spreading through a population). Experiments and numerical simulations show that the speed at which the wave moves is much slower than what is predicted by the deterministic, continuum equation. One way to resolve this discrepancy is to account for the role of noise in the model by adding a stochastic term in the equation (i.e. a stochastic partial differential equation). Analysis of the SPDE has shown that very small noise in the equation introduces a very large correction to the speed associated with the deterministic model. I will explain the basics of the deterministic and stochastic equations, and I will explain some ideas about the asymptotic analysis of the stochastic waves. I hope to have time to explain some open problems related to this topic.

**Category**: Graduate/Faculty Seminar**Duration**: 01:34:51**Date**: April 16, 2010 at 4:25 PM**Views**: 119-
**Tags:**seminar, Graduate/faculty Seminar

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