Acta mathematica scientia,Series B ›› 2000, Vol. 20 ›› Issue (2): 145-154.

• Articles •     Next Articles

LOCALIZATION AND APPROXIMATION OF ATTRACTORS FOR THE KURAMOTO-SIVASHINSKY EQUATIONS

 WU Yu-Jiang, GUO Ben-Yu   

  1. Department of Mathematics, Lanzhou University, Lanzhou 730000, China Department of Mathematics, Shanghai University, Jiading Campus, Shanghai 201800, China
  • Online:2000-04-18 Published:2000-04-18
  • Supported by:

    Project Supported by National Natural Science Foundation of China. Especially, the Work of the First Author was Supported Partially by the Science Foundation of the State Education Commission of China for the Returned Workers

Abstract:

The aim of this paper is to provide explicitly a sequence of m-dimensional approximate inertial manifolds Mm,j , j = 1, 2, · · · , for each positive integer m, for the Kuramoto-Sivashinsky equations. A very thin neighborhood into which the orbits enter with an exponential speed and in a finite time is associated with each manifold. The thickness of these neighborhoods decreases with increasing m for a fixed order j. Besides, the neighborhoods localize the global attractor and aid in the approximate computation of large-time solutions of the Kuramoto-Sivashinsky equations.

Key words: Kuramoto-Sivashinsky equations, attractors, approximate inertial manifolds

CLC Number: 

  • 34C40
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