2018/05/11 by Kuroda, Takanori, Ôtani, Mitsuharu
#35K61 #35Q56 #47J35 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1805.04312
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.