Initial-boundary value problems for complex Ginzburg-Landau equations governed by p-Laplacian in general domains

Abstract

In this paper, complex Ginzburg-Landau (CGL) equations governed by p-Laplacian
are studied. We discuss the global existence of solutions for the initial-boundary value
problem of the equation in general domains. The global solvability of the initialboundary
value problem for the case when p = 2 is already examined by several authors
provided that parameters appearing in CGL equations satisfy a suitable condition. Our
approach to CGL equations is based on the theory of parabolic equations with nonmonotone
perturbations. By using this method together with some approximate procedure
and a diagonal argument, the global solvability is shown without assuming any
growth conditions on the nonlinear terms.