Extended Fisher-Kolmogorov系统的整体吸引子及其分形维数估计

A Global Attractor of Extended Fisher-Kolmogorov System and Estimate to Fractal Dimention

考虑在一般情况下ExtendedFisher Kolmogorov(EFK)系统的解的长时间行为,利用解的存在唯一性和在H和V1空间的吸收集的存在性,证明了该系统在L2中的整体吸引子的存在性,并给出了其整体吸引子的分形维数估计.

In this paper, the long-time behaviour of solutions of Extended Fisher-Kolmogorov system is considered. It is proved that the system possesses a global attractor in terms of the existence and uniqueness of the solution. Then the existence of the absorbing set in the spaces H and V_1, and a two-side estimate for the fractal dimension of it is presented.