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 initial-boundary 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 non-monotone 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.