On The Small Dispersion Limit For A Special Class Of Complex Ginzburg-Landau Equations

In this paper we consider a special class of complex Ginzburg-Landau equations. We obtain sufficient conditions for the existence and uniqueness of global solutions for the initial value problem in d-dimensional torus T^d, and that solutions are approximated by solutions of the corresponding small dispersion limit equation for a period of time that goes to infinity as dispersive coefficient goes to zero. In present paper is divided into two parts.In chapter 1, we show the existence and uniqueness of global (in time) solution and the regularity of this solution for the. following complex Ginzburg-Landau equations:with initial value conditionhere are real numbers.In chapter 2, we show that the solution to problem (1), (2) is approximated in all W¹,p(T^d)-norm by solutions of the corresponding small dispersion limit equation for a period of time that goes to infinity as δ₂ goes to zero.