弱阻尼KdV方程的近似惯性流形

Approximate Inertial Manifolds for the Weakly Demped KdV Equations

本文给出了弱阻尼ＫｄＶ方程近似惯性流形族的一个构造方法，得到的近似惯性流形是一个弱Ｌｉｐｓｃｈｉｔｚ连续的流形，它对吸引子的指数渐近速率比平坦惯性流形相应的速率要高．

The existence and structure of inertial manifolds for eakly dissipative evolutionary equations are still not known. In this paper we give a way to construct a family of approximate inertial manifolds for weakly damped KdV equations. Approximate inerital manifolds we got are weakly Lipschitz contiuous , and approximate the attractor rapily.