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

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