Kolmogorov-Spieqel-Sivashinsky方程的渐近吸引子及维数估计The asymptotic attractor and dimensional estimate of Kolmogorov-Spieqel-Sivashinsky equation
周萍;邢超;罗宏;
摘要(Abstract):
研究了周期边界条件下Kolmogorov-Spieqel-Sivashinsky方程的渐近吸引子,并给出了它的维数估计.首先利用正交分解法构造了一个有限维解序列,然后分两步证明该解序列收敛于方程的真实解.
关键词(KeyWords): Kolmogorov-Spieqel-Sivashinsky方程;渐近吸引子;维数估计
基金项目(Foundation): 国家自然科学基金(11271271);; 四川省科技计划项目(2015JY0125)
作者(Authors): 周萍;邢超;罗宏;
参考文献(References):
- [1]Depassier M C,Spiegel E A.The large-scale structure of compressible convection[J].The Astronomical Journal,1981,86(3):496-512.
- [2]Depassier M C.A note on the free boundary conditions in Rayleigh-Bernard convection between insulating boundaries[J].Phys.Lett,1984,102A(8):359-361.
- [3]Poyet J P.The Rayleigh-Benard two-dimensional convection in a fluid between two plates of finite conductivity[D].New York:Columbia University,1983.
- [4]Guo B L,Wang B X.Long-time behaviour of the solution for the multidimensional Kolmogorov-SpieqelSivashinsky equation[J].Acta Mathematica Sinica(English Series),2002,18(3):579-596.
- [5]王冠香,刘曾荣.Kuramoto-Sivashinsky方程的渐近吸引子[J].应用数学学报,2000,23(3):329-336.
- [6]罗宏,蒲志林.Extended Fisher-Kolmogorov系统的渐近吸引子[J].纯粹数学与应用数学,2004,20(2):150-156.
- [7]何素芳,朱朝生.推广的B-BBM方程的渐近吸引子[J].四川师范大学学报:自然科学版,2007,30(1):49-52.
- [8]Zhao L N,Zhang X Y,Xing T L.The asymptotic attractor of 2D Navier-Stokes equation[J].数学研究,2007,40(3):251-257.
- [9]张晓明,姜金平,董超雨.Kdv-Burgers-Kuramoto系统的渐近吸引子[J].纯粹数学与应用数学,2014,30(6):595-603.
- [10]张晓明,姜金平,董超雨.非线性梁方程的渐近吸引子[J].数学的实践与认识,2015,45(2):302-308.