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.
"A Two-Dimensional Landau-Lifshitz Model in Studying Thin Film Micromagnetics." Abstr. Appl. Anal. 2009 1 - 13, 2009. https://doi.org/10.1155/2009/603591