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Front Propagation in Random Drift
PDE Seminar| Speaker: | Jim Nolan, Stanford University |
| Location: | 1147 MSB |
| Start time: | Fri, May 11 2007, 12:10PM |
Some reaction-advection-diffusion equations admit traveling wave solutions; these are simplified models of an animal population or combustion reaction spreading with constant speed. Even when the medium is random, solutions to the initial value problem may develop fronts propagating with a well-defined speed. In this presentation, I will describe recent work on front propagation in a random drift when the nonlinearity is the Kolmogorov-Petrovsky-Piskunov (KPP) type nonlinearity. The result is a representation of the front speed in terms of large deviations estimates for the related diffusion processes in a random environment. This extends a well-known representation for the speed in deterministic media. I also will discuss some analytical bounds on the front speed that can be derived from this representation.