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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 747092, 9 pages
http://dx.doi.org/10.1155/2014/747092
Research Article

Exact Boundary Controller Design for a Kind of Enhanced Oil Recovery Models

1State Key Lab of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China
2Department of Mathematics, Zhejiang University, Hangzhou 310027, China
3Department of Mathematics, College of Science, Southwest Petroleum University, Chengdu 610500, China

Received 23 October 2013; Revised 23 December 2013; Accepted 29 December 2013; Published 17 February 2014

Academic Editor: Stanislaw Migorski

Copyright © 2014 Ping Guo 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 exact boundary controllability of a class of enhanced oil recovery systems is discussed in this paper. With a simple transformation, the enhanced oil recovery model is first affirmed to be neither genuinely nonlinear nor linearly degenerate. It is then shown that the enhanced oil recovery system with nonlinear boundary conditions is exactly boundary controllable by applying a constructed method. Moreover, an interval of the control time is presented to not only give the optimal control time but also show the time for avoiding the blowup of the controllable solution. Finally, an example is given to illustrate the effectiveness of the proposed criterion.