Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic EquationReport as inadecuate




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Journal of Applied MathematicsVolume 2013 2013, Article ID 353757, 8 pages

Research ArticleSchool of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, China

Received 17 December 2012; Revised 15 May 2013; Accepted 30 May 2013

Academic Editor: Roberto Natalini

Copyright © 2013 Yu-Zhu Wang. 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

We consider the Cauchy problem for the damped nonlinear hyperbolic equation in n-dimensional space. Under small condition on the initial value, the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces are obtained by the contraction mapping principle.





Author: Yu-Zhu Wang

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



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