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N. Akroune. Regularity of the attractor for a weakly damped nonlinear Schrodinger equation on . Applied Mathematics Letters, 1999, 12(1): 45-48.

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• 标题: 半离散Kuramoto-Sivashinsky方程的全局吸引子Global Attractor for Semi-Discrete Kuramo-to-Sivashinsky Equation

  作者: 董胜楠, 朱朝生

  关键字: Kuramoto-Sivashinsky方程, Crank-Nicolson格式, 全局吸引子Kuramoto-Sivashinsky Equation; Crank-Nicolson Scheme; Global Attractor

  期刊名称: 《Pure Mathematics》, Vol.3 No.3, 2013-05-24

  摘要: 本文研究在上具有周期边界条件的半离散Kuramoto-Sivashinsky型方程解的长时间行为。首先利用Crank-Nicolson格式对其进行离散，然后证明了该方程在和上紧的全局吸引子的存在。We study the long-time behaviour with a periodical boundary condition of semi-discrete Kuramoto- Sivashinsky equation in First, we use the Crank-Nicolson scheme to discrete this equation to prove that such a semi-discrete equation possesses a global arrtactor in , then we also show that this global attractor is actually a compact set of and .