Zusammenfassung für den Vortrag am 27.10.1998 (16:45 Uhr)Oberseminar ANALYSIS
Reiner Schaetzle (Universität Freiburg)
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.