Asymptotic Behavior of the Initial-boundary Value Problem of Landau-Lifshitz-Schrodinger Type

This paper is concerned with the asymptotic behavior of the classical solutions of a Landau-Lifshitz-Schrodinger-type problem with initial-boundary values when the parameter epsilon goes to zero. We establish several uniform estimates of u(epsilon) by a conservation result and the standard parabolic method. Based on these results, we obtain parabolic behavior in the dissipative case and non-parabolic behavior of the semi-classical limits of those solutions respectively.