Large time asymptotic behaviour of solutions of the complex Landau-Ginzburg equation

The asymptotic behaviour for large time of solutions of the Cauchy problem for the complex Landau-Ginzburg equation is described. The initial data are assumed to be small in the multidimensional case (relative to the space variables), and they can be arbitrary in the one-dimensional case. In both cases the leading term is explicitly presented and an estimate for the remainder in the uniform metric is given