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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 715959, 8 pages
http://dx.doi.org/10.1155/2013/715959
Research Article

Optimal Control of a Viscous Shallow Water Equation

1Taizhou Institute of Science and Technology (NUST) Taizhou, Jiangsu 225300, China
2Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 22 June 2013; Accepted 23 August 2013

Academic Editor: Shao-Ming Fei

Copyright © 2013 Wenbin Zhang and Jiangbo Zhou. 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

This paper is concerned with a viscous shallow water equation, which includes both the viscous Camassa-Holm equation and the viscous Degasperis-Procesi equation as its special cases. The optimal control under boundary conditions is given, and the existence of optimal solution to the equation is proved.