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

Authors: Guo, Bo; Wang, Bi

Source: Acta Mathematica Sinica, Volume 18, Number 3, July 2002 , pp. 579-596(18)

Publisher: Springer

Buy & download fulltext article:

Price: $47.00 plus tax (Refund Policy)

Abstract:

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 estimates 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.

Keywords: Global solution; Approximate inertial manifold; Gevrey class regularity; Kolmogorov-Spiegel-Sivashinsky equation; 35K57; 35B40; 35P10

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10114-002-0195-5

Affiliations: 1: Email: gbl@mail.iapcm.ac.cn

Publication date: 2002-07-01