Asymptotic behaviour of Ginzburg-Landau functionals
by
Andrija Raguz
Department of Mathematics, University of Zagreb and Max-Planck Institute for Mathematics in the Sciences, Leipzig

We consider one dimensional singularly perturbed problem which leads to multiple small scales depending on a small parametar \epsilon. Our goal is to describe the limiting behaviour of the functional

I\epsilon(v): ó õ \Omega  (\epsilon2 v''2+W(v')+a(v-g)2)  .

Functional I_\epsilon is a variation of a Cahn-Hilliard functional, namely the Ginzburg-Landau functional, which appears naturally in the Cahn-Hilliard model for phase transitions. We generalise a recent result by G. Alberti and S. Müller (which concerns the case g=0) to the case of arbitrary Lipschitz function g.

The approach relies on two important ingredients: rewriting the initial functional in terms of blow-ups of a function v and well-known \Gamma-convergence result of L. Modica and S. Mortola.

Date received: March 15, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-20.