The Research Of Coupled Ginzburg-Landau Equations

Infinite dimensional dynamical systems play an extremely important role in non-linear science, Global attractor is a notation which can be used to describe the longtime behavior of the system. Global attractor is one of the infinite dimensional dynam-ical systems. The research on the global attractor lies in two respects. One respect isit's existence, another is it's geometric properties, such as Hausdor- dimension , Frac-tal dimension and upper continuity and so on. This paper researches a class infinitedimensional systems - Ginzburg - Landau equations (later referred to as the G - -Lequations) with great significance in practice, and gets Hausdor- dimension's supre-mum and Fractal dimension's supremums of G - L equations'global attractor ,provesthe global attractors'existence of the space discretization Ginzburg-Landau equations.Main results can be divided into the following three parts.In first chapter first introduces the backgroud of G-L equations,the author's mainresearch works; on the one hand, the paper introduces absorbing sets'definition,globalattractor and it's dimension definitions ; on the other hand, the paper applies the theo-rem of global attractors'existence and the conclusion of dimension estimate .In second chapter considers Ginzburg - Landau equations, By using the overalland individual variable substitution ways,the author estimate the dimension of globalattractors,hence get di-erent supremums of the dimension and make the appropriatecomparison of the two supremums.In third chapter ,the author research the space discretization Ginzburg - Landauequations and get existence of the global attractors.