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The Scientific World Journal
Volume 2014 (2014), Article ID 716740, 10 pages
http://dx.doi.org/10.1155/2014/716740
Research Article

Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation

1Department of Mathematics, Pusan National University, 30 Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea
2Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA
3Department of Cogno-Mechatronics Engineering and School of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of Korea

Received 23 January 2014; Accepted 23 February 2014; Published 7 April 2014

Academic Editors: D. Baleanu and H. Jafari

Copyright © 2014 Daewook Kim et al. 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

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form under suitable assumptions on , and . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation . Lastly, numerical simulations in order to verify the analytical results are given.