Table of Contents
International Journal of Partial Differential Equations
Volume 2013, Article ID 424309, 7 pages
http://dx.doi.org/10.1155/2013/424309
Research Article

Approximate Controllability of a Semilinear Heat Equation

1Universidad de Los Andes, Facultad de Ciencias, Departamento de Matemática, Mérida 5101, Venezuela
2Universidad Central de Venezuela, Facultad de Ciencias, Departamento de Matemática, Caracas 1051, Venezuela

Received 8 April 2013; Accepted 11 September 2013

Academic Editor: Michael Grinfeld

Copyright © 2013 Hugo Leiva 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. D. Barcenas, H. Leiva, and Z. Sivoli, “A broad class of evolution equations are approximately controllable, but never exactly controllable,” IMA Journal of Mathematical Control and Information, vol. 22, no. 3, pp. 310–320, 2005. View at Google Scholar
  2. J. I. Díaz, J. Henry, and A. M. Ramos, “On the approximate controllability of some semilinear parabolic boundary-value problems,” Applied Mathematics and Optimization, vol. 37, no. 1, pp. 71–97, 1998. View at Google Scholar · View at Scopus
  3. E. Fernandez-Cara, “Remark on approximate and null controllability of semilinear parabolic equations,” vol. 4, pp. 73–81, Proceedings of the Controle et Equations aux Derivees Partielles (ESAIM '98), 1998.
  4. E. Fernández-Cara and E. Zuazua, “Controllability for blowing up semilinear parabolic equations,” Comptes Rendus de l'Academie des Sciences I, vol. 330, no. 3, pp. 199–204, 2000. View at Google Scholar · View at Scopus
  5. H. Leiva, N. Merentes, and J. L. Sanchez, “Interior controllability of the nD semilinear heat equation,” African Diaspora Journal of Mathematics, vol. 12, no. 2, pp. 1–12, 2011, Special vol. in Honor of Profs. C. Corduneanu, A. Fink, and S. Zaidman. View at Google Scholar
  6. H. Leiva, N. Merentes, and J. Sanchez, “Approximate controllability of semilinear reaction diffusion,” Mathematical Control and Ralated Fields, vol. 2, no. 2, 2012. View at Google Scholar
  7. H. Leiva, N. Merentes, and J. Sanchez, “A characterization of semilinear dense range operators and applications,” Abstract and Applied Analysis, vol. 2013, Article ID 729093, 11 pages, 2013. View at Publisher · View at Google Scholar
  8. X. Zhang, “A remark on null exact controllability of the heat equation,” SIAM Journal on Control and Optimization, vol. 40, no. 1, pp. 39–53, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. E. Zuazua, “Controllability of a system of linear thermoelasticity,” Journal de Mathématiques Pures et Appliquées, vol. 74, pp. 291–315, 1995. View at Google Scholar
  10. E. Zuazua, “Controllability of partial differential equations and its semi-discrete approximations,” Discrete and Continuous Dynamical Systems, vol. 8, no. 2, pp. 469–513, 2002. View at Google Scholar · View at Scopus
  11. H. Leiva and Y. Quintana, “Interior controllability of a broad class of reaction diffusion equations,” Mathematical Problems in Engineering, vol. 2009, Article ID 708516, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Brezis, Analisis Funcional, Teoria y Applicaciones, Alianza Universitaria Textos, Masson, Paris, 1983; cast.: Alinza Editorial, S. A., Madrid, Spain, 1984.
  13. G. Isac, “On Rothe’s fixed point theorem in general topological vector space,” Analele Stiintifice ale Universitatii Ovidius Constanta, vol. 12, no. 2, pp. 127–134, 2004. View at Google Scholar
  14. M. H. Protter, “Unique continuation for elliptic equations,” Transaction of the American Mathematical Society, vol. 95, no. 1, 1960. View at Google Scholar
  15. R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems, vol. 8 of Lecture Notes in Controland Information Sciences, Springer, Berlin, Germany, 1978.
  16. C. E. Lawrence, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, American Mathematical Society, 1999.
  17. C. Kesavan, Topics in: Functional Analysis and Applications, John Wiley & Sons, 1989.
  18. R. F. Curtain and H. J. Zwart, An Introduction to Infinite Dimensional Linear Systems Theory, vol. 21 of Text in Applied Mathematics, Springer, New York, NY, USA, 1995.
  19. D. Bárcenas, H. Leiva, and W. Urbina, “Controllability of the Ornstein-Uhlenbeck equation,” IMA Journal of Mathematical Control and Information, vol. 23, no. 1, pp. 1–9, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. D. Barcenas, H. Leiva, Y. Quintana, and W. Urbina, “Controllability of Laguerre and Jacobi equations,” International Journal of Control, vol. 80, no. 8, pp. 1307–1315, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. H. Leiva, N. Merentes, and J. L. Sanchez, “Interior controllability of the Benjamin-Bona-Mahony equation,” Journal of Mathematis and Applications, no. 33, pp. 51–59, 2010. View at Google Scholar