Asymptotic Theory Of Extended Fisher-Kolmogorov System

This paper deals with asymptotic theory and long-time behavior of solution of Extended Fisher-Kolmogorov system. In Capter 2, it is proved that the system possesses a global attractor and a two-side estimate for the fractal dimension of it is presented. In Capter 3, several different approximate intertial manifolds of the system are constructed by applying linear Galerkin method, method of projecting operator and operator eigenvalue and successive iterative method, and it is proved that arbitary trajectory of the system enters into a small neighbourhood of the global attractor after large time. Capter 4 studies the asymptotic attractor of the system by constructing a solution sequence which approaches to the global attractor of the equation in long time, and the dimentional estimate of the asymptotic attractor is given.