二维Extended Fisher-Kolmogorov方程的渐近吸引子及维数估计  

The Asymptotic Attractor and Dimensional Estimate of Two Dimensional Extended Fisher-Kolmogorov Equation

作　　者：周萍[1] 邢超[1] 罗宏[1] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610066

出　　处：《重庆师范大学学报（自然科学版）》2017年第1期61-68,共8页Journal of Chongqing Normal University:Natural Science

基　　金：四川省科技计划项目(No.2015JY0125)

摘　　要：【目的】研究二维周期边界条件下Extended Fisher-Kolmogorov方程的渐近吸引子,并给出它的维数估计。【方法】利用正交分解、能量估计等方法对此进行讨论。【结果】构造了一个有限维解序列,并证明该解序列不会远离方程的吸收集。【结论】最后通过证明解序列趋近于真实解,从而可以得出方程渐近吸引子的存在性。[Purposes]In this paper,the asymptotic attractor of 2D Extended Fisher-Kolmogorov equation with periodic boundary conditions was studied,and the dimensional estimate of the asymptotic attractor was obtained.[Methods]It is discussed by using the orthogonal decomposition,the energy estimate method and so on.[Findings]A finite dimensional solution sequence was constructed,and proves that the solution sequence doesn＇t go away from the absorbing set.[Conclusions]Finally,it is shown that the solution sequence approaches to the real solution,so the existence of the asymptotic attractor is proved.

关 键 词：二维Extended Fisher-Kolmogorov方程 渐近吸引子 维数估计 

分 类 号：O175.26[理学—数学]