Talk
Gamma-Limit for the Extended Fisher-Kolmogorov equation
- Reiner Schaetzle (Universität Freiburg)
Abstract
We consider the Extended Fisher-Kolmogorov equation
where 
is a double-well potential and γ>0. For γ=0 this is the ordinary Allen-Cahn equation. The equation for the stationary waves is the ordinary differential equation 
with appropriate boundary conditions. In this talk, we present estimates on the second derivatives of solutions of (2) which enable to prove that bumps of these solutions have to have a minimal size, hence cannot accumulate.
As main result, we prove that the area functional is the Γ-Limit of 
which is a Ljapunov functional of (1).
This is joint work with Danielle Hilhorst and Lambert A. Peletier.
