Year: 2004
Author: Xinmin Xiang
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 1 : pp. 89–100
Abstract
Klein-Gordon-Schrödinger (KGS) equations are very important in physics. Some papers studied their well-posedness and numerical solution [1-4], and another works investigated the existence of global attractor in $R^n$ and $\Omega ⊂ R^n \ (n\leq 3)$ [5-6,11-12]. In this paper, we discuss the dynamical behavior when we apply spectral method to find numerical approximation for periodic initial value problem of KGS equations. It includes the existence of approximate attractor $A_N$, the upper semi-continuity on $A$ which is a global attractor of initial problem and the upper bounds of Hausdorff and fractal dimensions for $A$ and $A_N$, etc.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JCM-10337
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 1 : pp. 89–100
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Klein-Gordon-Schrödinger equation Spectral approximate Global attractor Hausdorff dimension Fractal dimension.