ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS

doi:10.1016/S0252-9602(12)60190-8

Abstract

Abstract:

A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L² ×H¹ ×H² over a finite time interval (0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.

Key words: dissipative Zakharov equations, dynamical system, global attractor, finite difference method

CLC Number:

65M06

ZHANG Fa-Yong, GUO Bai-Ling. ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS[J].Acta mathematica scientia,Series B, 2012, 32(6): 2431-2452.

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