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Journal of Applied Mathematics
Volume 2014, Article ID 127809, 13 pages
Research Article

Quenching Time Optimal Control for Some Ordinary Differential Equations

School of Mathematics & Statistics, Northeast Normal University, Changchun 130024, China

Received 23 January 2014; Accepted 28 February 2014; Published 10 April 2014

Academic Editor: Alberto Cabada

Copyright © 2014 Ping Lin. 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.


This paper concerns time optimal control problems of three different ordinary differential equations in . Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to control the systems is to minimize the quenching time. The purpose of this study is to obtain the existence and the Pontryagin maximum principle of optimal controls. The methods used in this paper adapt to more general and complex ordinary differential control systems with quenching property. We also wish that our results could be extended to the same issue for parabolic equations.