耗散KDV型方程的渐近吸引子

摘 要:本文考虑了耗散KDV型方程 的渐近吸引子,即构造了一个有限维解序列.首先利用数学归纳法证明了该解序列不会远离方程的整体吸引子;其次,证明了它在长时间后无限趋于方程的整体吸引子, 并且给出了渐近吸引子的维数估计.

Asymptotic Attractor of Dissiptive KDV type Equation

In this paper,we study the long time behaviour of solution of dissipative KDV type equation by constructing a solution sequence.At first,we prove that the solution sequence doesn´t go away from the global attractor in terms of mathema-tical induction;the second, We give that the solution sequence approaches to the global attractor of the equation in long time and the dimensional estimate of the asymptotic attractor.