Neumann inhomogeneous boundary value problem for the n+1 complex Ginzburg-Landau equation

We study the following Neumann inhomogeneous boundary value problem for the complex Ginzburg-Landau equation on 0 subset of R-n(n <= 3) : u(t), = (a + i alpha)Att - (b + i beta)vertical bar u vertical bar 1112 u(a, b, t > 0) under initial condition u(x, 0) = h(x) for x E Omega and Neumann boundary condition partial derivative n/partial derivative/n=K(x, t) on W partial derivative where h, K are given functions. Under suitable conditions, we prove the existence of a global solution in H-1. (C) 2006 Elsevier Inc. All rights reserved.