Reaction-diffusion fronts in random and heterogeneous media

Lenya Rhyzik

University of Chicago
ABSTRACT:

It is well known that scalar reaction-diffusion equations in
homogeneous media admit special planar front solutions which propagate
with a constant speed. They are stable for a large class of
nonlinearities. Similar results have been established in periodic media
by Berestycki and Hamel, and Weinberger. I will discuss generalizations
of the notion of a traveling front to general heterogeneous media and,
inparticular, random media, as well as stability of those fronts when
the nonlinearity is of the ignition type. This is ajoint work with J.
Nolen, J.-M. Roquejoffe and A. Mellet.