Nonhomogeneous Boundary Value Problems For The Complex Ginzburg-Landau Equation Posed On A Finite Interval

This paper is concerned with the well-posedness of the complex Ginzburg-Landau equation posed on a finite interval (0, L) with nonhomogeneous Dirichlet boundary conditions. When the initial datum belongs to H-s(0, L) (-1/2 < s <= 0) and the boundary data belong to some subspace of H s/2 + 1/4 (0, T), the complex Ginzburg-Landau equation is shown to be globally well-posed.