EXISTENCE AND NON-EXISTENCE OF GLOBAL SOLUTIONS FOR THE SEMILINEAR COMPLEX GINZBURG-LANDAU TYPE EQUATION IN HOMOGENEOUS AND ISOTROPIC SPACETIME

Abstract

The Cauchy problem for the semilinear complex Ginzburg-Landau type equation is considered in homogeneous and isotropic spacetime. Global solutions and their asymptotic behaviours for small initial data are obtained. The non-existence of non-trivial global solutions is also shown. The effects of spatial expansion and contraction are studied through the problem.