Uniform Attractor and Approximate Inertial Manifolds for Nonautonomous Long-Short Wave EquationsReport as inadecuate




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Abstract and Applied AnalysisVolume 2013 2013, Article ID 830715, 17 pages

Research Article

School of Mathematics and Statistics Science, Ludong University, Yantai 264025, China

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received 28 August 2013; Revised 17 October 2013; Accepted 18 October 2013

Academic Editor: Carlo Bianca

Copyright © 2013 Hongyong Cui and Jie Xin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Nonautonomous long-short wave equations with quasiperiodic forcesare studied. We prove the existence of the uniform attractor for the system by means of energymethod, which is widely used to deal with problems who have no continuity with respectto the initial data property, as well as to those which Sobolev compact imbedding cannotbe applied. Afterwards, we construct an approximate inertial manifold by means of extendingphase space method and we estimated the size of the corresponding attracting neighborhoodfor this manifold.





Author: Hongyong Cui and Jie Xin

Source: https://www.hindawi.com/



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