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Volume 22, Issue 1
The Long-Time Behavior of Spectral Approximate for Klein-Gordon-Schrödinger Equations

Xinmin Xiang

J. Comp. Math., 22 (2004), pp. 89-100.

Published online: 2004-02

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  • 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.

  • Keywords

Klein-Gordon-Schrödinger equation, Spectral approximate, Global attractor, Hausdorff dimension, Fractal dimension.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-89, author = {Xiang , Xinmin}, title = {The Long-Time Behavior of Spectral Approximate for Klein-Gordon-Schrödinger Equations}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {1}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10337.html} }
TY - JOUR T1 - The Long-Time Behavior of Spectral Approximate for Klein-Gordon-Schrödinger Equations AU - Xiang , Xinmin JO - Journal of Computational Mathematics VL - 1 SP - 89 EP - 100 PY - 2004 DA - 2004/02 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10337.html KW - Klein-Gordon-Schrödinger equation, Spectral approximate, Global attractor, Hausdorff dimension, Fractal dimension. AB -

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.

Xiang , Xinmin. (2004). The Long-Time Behavior of Spectral Approximate for Klein-Gordon-Schrödinger Equations. Journal of Computational Mathematics. 22 (1). 89-100. doi:
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