半离散Kuramoto-Sivashinsky方程的全局吸引子

Global Attractor for Semi-Discrete Kuramo-to-Sivashinsky Equation

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 .