THE LONG-TIME BEHAVIOR OF SPECTRAL APPROXIMATE FOR KLEIN-GORDON-SCHROEDINGER EQUATIONS

Klein-Gordon-Schroedinger (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 Ω包含于R^n (n≤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 AN, 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 AN,etc.

The Long-Time Behavior of Spectral Approximate for Klein-Gordon-Schrödinger Equations

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 $Omega ⊂ R^n (nleq 3)$ [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.