Abstract and Applied Analysis
Volume 2009 (2009), Article ID 603591, 13 pages
doi:10.1155/2009/603591
Research Article

A Two-Dimensional Landau-Lifshitz Model in Studying Thin Film Micromagnetics

Jingna Li

Department of Mathematics, Jinan University, Guangzhou 510632, China

Received 26 November 2008; Accepted 6 February 2009

Academic Editor: Nicholas Alikakos

Copyright © 2009 Jingna Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper is concerned with a two-dimensional Landau-Lifshitz equation which was first raised by A. DeSimone and F. Otto, and so fourth, when studying thin film micromagnetics. We get the existence of a local weak solution by approximating it with a higher-order equation. Penalty approximation and semigroup theory are employed to deal with the higher-order equation.