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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 585967, 10 pages
http://dx.doi.org/10.1155/2015/585967
Research Article

Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone

State Key Laboratory of Synthetical Automation for Process industries, Northeastern University, Shenyang 110004, China

Received 1 November 2014; Revised 16 December 2014; Accepted 8 January 2015

Academic Editor: Ricardo Weder

Copyright © 2015 Yuan Wang 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.

Linked References

  1. V. Bratu, C. Mortici, C. Oros, and N. Ghiban, “Mathematical model of solidification process in steel continuous casting taking into account the convective heat transfer at liquid-solid interface,” Computational Materials Science, vol. 94, pp. 2–7, 2014. View at Publisher · View at Google Scholar · View at Scopus
  2. A. V. Lotov, G. K. Kamenev, V. E. Berezkin, and K. Miettinen, “Optimal control of cooling process in continuous casting of steel using a visualization-based multi-criteria approach,” Applied Mathematical Modelling, vol. 29, no. 7, pp. 653–672, 2005. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Bergounioux and K. Kunisch, “Primal-dual strategy for state-constrained optimal control problems,” Computational Optimization and Applications, vol. 22, no. 2, pp. 193–224, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. W. Liu and N. Yan, Adaptive Finite Element Methods for Optimal Control Governed by PDEs, Science Press, Beijing, China, 2008.
  5. M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich, Optimization with PDE Constraints, Springer, 2009. View at MathSciNet
  6. J. Stafford, E. Walsh, and V. Egan, “A study on the flow field and local heat transfer performance due to geometric scaling of centrifugal fans,” International Journal of Heat and Fluid Flow, vol. 32, no. 6, pp. 1160–1172, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Renardy, W. J. Hursa, and J. A. Nohel, Mathematical in Viscoelasticity, Wiley, 1987.
  8. D. Hömberg, K. Krumbiegel, and J. Rehberg, “Optimal control of a parabolic equation with dynamic boundary condition,” Applied Mathematics and Optimization, vol. 67, no. 1, pp. 3–31, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. M. M. Kostreva and A. L. Ward, “Optimal control of a system governed by an elliptic partial differential equation,” Journal of Computational and Applied Mathematics, vol. 114, no. 1, pp. 173–187, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. H. Y. Li, “Estimation of thermal properties in combined conduction and radiation,” International Journal of Heat and Mass Transfer, vol. 42, no. 3, pp. 565–572, 1998. View at Publisher · View at Google Scholar · View at Scopus
  11. K. H. Lee, S. W. Baek, and K. W. Kim, “Inverse radiation analysis using repulsive particle swarm optimization algorithm,” International Journal of Heat and Mass Transfer, vol. 51, no. 11-12, pp. 2772–2783, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. M. H. Farag, F. H. Riad, and W. A. Hashem, “A penalty/MPQI method for constrained parabolic optimal control problems,” International Journal of Computer Science, vol. 2, pp. 635–648, 2014. View at Google Scholar
  13. M. Kaya and A. Erdem, “Simultaneous reconstruction of the source term and the surface heat transfer coefficient,” Mathematical Methods in the Applied Sciences, vol. 11, pp. 176–186, 2012. View at Google Scholar
  14. A. Hasanov, “Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: weak solution approach,” Journal of Mathematical Analysis and Applications, vol. 330, no. 2, pp. 776–779, 2007. View at Publisher · View at Google Scholar
  15. A. Hasanov, “An inverse source problem with single Dirichlet type measured output data for a linear parabolic equation,” Applied Mathematics Letters, vol. 24, no. 7, pp. 1269–1273, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. A. Hasanov and B. Pektaş, “Identification of an unknown time-dependent heat source term from overspecified Dirichlet boundary data by conjugate gradient method,” Computers & Mathematics with Applications, vol. 65, no. 1, pp. 42–57, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. C. A. Santos, J. A. Spim, and A. Garcia, “Mathematical modeling and optimization strategies (genetic algorithm and knowledge base) applied to the continuous casting of steel,” Engineering Applications of Artificial Intelligence, vol. 16, no. 5-6, pp. 511–527, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. B. You, M. Kim, D. Lee, J. Lee, and J. S. Lee, “Iterative learning control of molten steel level in a continuous casting process,” Control Engineering Practice, vol. 19, no. 3, pp. 234–242, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. N. Cheung, C. A. Santos, J. A. Spim, and A. Garcia, “Application of a heuristic search technique for the improvement of spray zones cooling conditions in continuously cast steel billets,” Applied Mathematical Modelling, vol. 30, no. 1, pp. 104–115, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. I. E. Livieris and P. Pintelas, “Globally convergent modified Perry's conjugate gradient method,” Applied Mathematics and Computation, vol. 218, no. 18, pp. 9197–9207, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus