Long-Time Behaviour of the Solutions for the Multidimensional Kolmogorov-Spieqel-Sivashinsky Equation  

作　　者：Bo Ling GUO Bi Xiang WANG Institute of Applied Physics and Computational Mathematics, P. O. Box 8009. Beijing 100088. P. R. China 

出　　处：《Acta Mathematica Sinica,English Series》2002年第3期579-596,共18页数学学报（英文版）

摘　　要：In this paper, we study the existence and long-time behaviour of the solutions for the multidimensional Kolmogorov-Spiegel-Sivashinsky equation. We first show the existence of the global solution for this equation, and then prove the existence of the global attractor and establish the esti- mates of the upper bounds of Hausdorff and fractal dimensions for the attractor. We also obtain the Gevrey class regularity for the solutions and construct an approximate inertial manifold for the system.In this paper, we study the existence and long-time behaviour of the solutions for the multidimensional Kolmogorov-Spiegel-Sivashinsky equation. We first show the existence of the global solution for this equation, and then prove the existence of the global attractor and establish the esti- mates of the upper bounds of Hausdorff and fractal dimensions for the attractor. We also obtain the Gevrey class regularity for the solutions and construct an approximate inertial manifold for the system.

关 键 词：Global solution Approximate inertial manifold Gevrey class regularity Kolmogorov-Spiegel-Sivashinsky equation 

分 类 号：O175[理学—数学]