Propagating terrace in one-dimensional semilinear diffusion equations.

Thursday, September 27, 2012 - 2:00pm - 2:50pm
Keller 3-180
Hiroshi Matano (University of Tokyo)
In this talk, I will discuss the front propagation for solutions of one-dimensional diffusion equations on the whole line:

u_t = u_{xx} + f(x,u).

Here f(x,u) is a smooth function that is periodic in x and satisfies f(x,0) = 0. We consider a large class of nonlinearities f including multistable ones. Our analysis reveals some new dynamics where the asymptotic profile of the solution is not characterized by a single front, but by a layer of several fronts traveling at different speeds, which we call a propagating terrace.

This is joint work with Thomas Giletti and Arnaud Ducrot.
MSC Code: