Weak and regular solutions for Landau-Lifschitz equations: existence and asymptotic behaviour

In this talk, we describe existence results for weak and regular solutions of Landau-Lifschitz equations. Furthermore, we present two types of asymptotic behaviour : for large time, we study the $\omega$-limit set of the weak solutions. On the other hand, we perform an asymptotic expansion of the regular solutions when the exchange coefficient goes to zero : it appears a boundary layer described with a BKW method.