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Journal of Applied Mathematics
Volume 2014, Article ID 127809, 13 pages
http://dx.doi.org/10.1155/2014/127809
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.

Linked References

  1. H. Kawarada, “On solutions of initial-boundary problem for ut=uxx+1/(1-u),” Publications of the Research Institute for Mathematical Sciences, vol. 10, no. 3, pp. 729–736, 1975. View at Publisher · View at Google Scholar · View at MathSciNet
  2. C. Y. Chan and H. G. Kaper, “Quenching for semilinear singular parabolic problems,” SIAM Journal on Mathematical Analysis, vol. 20, no. 3, pp. 558–566, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. V. Barbu, Analysis and Control of Nonlinear Infinite-Dimensional Systems, vol. 190, Academic Press, Boston, Mass, USA, 1993. View at MathSciNet
  4. H. O. Fattorini, Infinite Dimensional Linear Control Systems. The Time Optimal and Norm Optimal Problems, vol. 201, Elsevier Science, Amsterdam, The Netherlands, 2005. View at MathSciNet
  5. X. J. Li and J. M. Yong, Optimal Control Theory for Infinite-Dimensional Systems, Birkhäuser, Boston, Mass, USA, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  6. S. Luan, H. Gao, and X. Li, “Optimal control problem for an elliptic equation which has exactly two solutions,” Optimal Control Applications & Methods, vol. 32, no. 6, pp. 734–747, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. G. Zheng and B. Ma, “A time optimal control problem of some linear switching controlled ordinary differential equations,” Advances in Difference Equations, vol. 2012, article 52, 7 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  8. P. Lin and G. Wang, “Blowup time optimal control for ordinary differential equations,” SIAM Journal on Control and Optimization, vol. 49, no. 1, pp. 73–105, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. P. Lin, “Quenching time optimal control for some ordinary differential equations,” http://arxiv.org/abs/1209.0784. In press.