Nonhomogeneous boundary value problems for the complex Ginzburg–Landau equation posed on a finite interval

Abstract

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 () and the boundary data belong to some subspace of , the complex Ginzburg–Landau equation is shown to be globally well-posed.