Gamma-Limit for the Extended Fisher-Kolmogorov equation

We consider the Extended Fisher-Kolmogorov equation

where is a double-well

potential and .

For 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 Limit of

which is a Ljapunov functional of (1).

This is joint work with Danielle Hilhorst and Lambert A. Peletier.