On the global existence and small dispersion limit for a class of complex ginzburg-landau equations

摘要

In this paper we consider a class of complex Ginzburg-Landau equations. We obtain sufficient conditions for the existence and uniqueness of global solutions for the initial-value problem in d-dimensional torus Td, and that solutions are initially approximated by solutions of the corresponding small dispersion limit equation for a period of time that goes to infinity as dispersive coefficient goes to zero.