Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity-Reference-Cited by-同舟云学术

Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity

Published:2011 Issue: Volume:2011 Page:1-21
ISSN:0161-1712
Container-title:International Journal of Mathematics and Mathematical Sciences
language:en
Short-container-title:International Journal of Mathematics and Mathematical Sciences

Author:

Zhang Zai-yun¹²,Liu Zhen-hai³

Affiliation:

1. School of Mathematical Science and Computing Technology, Central South University, Changsha 410075, Hunan, China

2. Department of Mathematics and Science, Hunan First Normal University, Feng Lin San Lu 1015, Changsha 410205, Hunan, China

3. School of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, Guangxi, China

Abstract

We discuss global attractor for the generalized dissipative KDV equation with nonlinearity under the initial conditionu(x,0)=u0(x). We prove existence of a global attractor in spaceH2(Ω), by using decomposition method with cut-off function andKuratowskiα-measure in order to overcome the noncompactness of the classical Sobolev embedding.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Mathematics (miscellaneous)

Link

http://downloads.hindawi.com/journals/ijmms/2011/725045.pdf

Reference27 articles.

1. Estimate on the Dimension of Global Attractor for Nonlinear Dissipative Kirchhoff Equation

2. Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time

3. Global attractor and its dimension estimates for the generalized dissipative KdV equation onR