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Abstract and Applied Analysis
Volume 2008 (2008), Article ID 127394, 13 pages
http://dx.doi.org/10.1155/2008/127394
Research Article

State Trajectories Analysis for a Class of Tubular Reactor Nonlinear Nonautonomous Models

1Center de Recherche INRIA Futurs-Site de Bordeaux-IMB, 351 Cours de la Libération, Talent Cedex, Bordeaux 33405, France
2Département de Mathématique et Informatique, Faculté des Sciences, Université Chouaib Doukkali, El Jadida BP 20, Morocco

Received 4 July 2007; Accepted 3 September 2007

Academic Editor: Nicholas Dimitrios Alikakos

Copyright © 2008 B. Aylaj 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. Dochain, Contribution to the analysis and control of distributed parameter systems with application to (bio)chemical processes and robotics, M.S. thesis, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium, 1994.
  2. W. H. Ray, Advanced Process Control, Butterworths Series in Chemical Engineering, McGraw-Hill, Boston, Mass, USA, 1981.
  3. S. Renou, Commande Non-Linéaire d'un Systeme Décrit par des Equations Paraboliques: Application au Procédé de Blanchiment, M.S. thesis, Génie Chimique, Ecole Polytechnique de Montreal, Montreal, QC, Canada, 2000.
  4. S. Renou, M. Perrier, D. Dochain, and S. Gendron, “Solution of the convection-dispersion-reaction equation by a sequencing method,” Computers & Chemical Engineering, vol. 27, no. 5, pp. 615–629, 2003. View at Publisher · View at Google Scholar
  5. J. J. Winkin, D. Dochain, and P. Ligarius, “Dynamical analysis of distributed parameter tubular reactors,” Automatica, vol. 36, no. 3, pp. 349–361, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. E. Achhab, B. Aylaj, and M. Laabissi, “Global existence of state trajectoties for a class of tubular reactor nonlinear models,” in Proceedings CD-ROM of the 16th International Symposium on the Mathematical Theory of Networks and Systems (MTNS '04), Leuven, Belgium, July 2004.
  7. B. Aylaj, M. E. Achhab, and M. Laabissi, “Asymptotic behaviour of state trajectories for a class of tubular reactor nonlinear models,” IMA Journal of Mathematical Control and Information, vol. 24, no. 2, pp. 163–175, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  8. R. H. Martin Jr., “Mathematical models in gas-liquid reactions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 4, no. 3, pp. 509–527, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. N. D. Alikakos, “Lp Bounds of solutions of reaction-diffusion equations,” Communications in Partial Differential Equations, vol. 4, no. 8, pp. 827–868, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. K. Masuda, “On the global existence and asymptotic behavior of solutions of reaction-diffusion equations,” Hokkaido Mathematical Journal, vol. 12, no. 3, pp. 360–370, 1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. E. P. Van Elk, Gas-liquid reactions: influence of liquid bulk and mass transfer on process performance, M.S. thesis, University of Twente, Enschede, The Netherlands, 2001.
  12. P. V. Danckwerts, Gas-Liquid Reactions, McGraw-Hill, New York, NY, USA, 1970.
  13. R. F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, vol. 21 of Texts in Applied Mathematics, Springer, New York, NY, USA, 1995. View at Zentralblatt MATH · View at MathSciNet
  14. R. H. Martin Jr., Nonlinear Operators and Differential Equations in Banach Spaces, Pure and Applied Mathematics, John Wiley & Sons, New York, NY, USA, 1976. View at Zentralblatt MATH · View at MathSciNet
  15. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1983. View at Zentralblatt MATH · View at MathSciNet
  16. T. Iwamiya, “Global existence of mild solutions to semilinear differential equations in Banach spaces,” Hiroshima Mathematical Journal, vol. 16, no. 3, pp. 499–530, 1986. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. B. Aulbach and N. Van Minh, “Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolution equations,” Abstract and Applied Analysis, vol. 1, no. 4, pp. 351–380, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Editura Academiei Republicii Socialiste România, Bucharest, 1976. View at Zentralblatt MATH · View at MathSciNet
  19. D. Bothe, “Flow invariance for perturbed nonlinear evolution equations,” Abstract and Applied Analysis, vol. 1, no. 4, pp. 417–433, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Z.-H. Luo, B.-Z. Guo, and O. Morgul, Stability and Stabilization of Infinite Dimensional Systems with Applications, Communications and Control Engineering Series, Springer, London, UK, 1999. View at Zentralblatt MATH · View at MathSciNet
  21. C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, NY, USA, 1992. View at Zentralblatt MATH · View at MathSciNet
  22. N. Pavel, “Invariant sets for a class of semi-linear equations of evolution,” Nonlinear Analysis. Theory, Methods & Applications, vol. 1, no. 2, pp. 187–196, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. T. Iwamiya, “Global existence of solutions to nonautonomous differential equations in Banach spaces,” Hiroshima Mathematical Journal, vol. 13, no. 1, pp. 65–81, 1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. N. Kenmochi and T. Takahashi, “Nonautonomous differential equations in Banach spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 4, no. 6, pp. 1109–1121, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. W. Arendt, A. Grabosch, G. Greiner et al., One-Parameter Semigroups of Positive Operators, vol. 1184 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1986. View at Zentralblatt MATH · View at MathSciNet
  26. M. Laabissi, M. E. Achhab, J. J. Winkin, and D. Dochain, “Multiple equilibrium profiles for nonisothermal tubular reactor nonlinear models,” Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms, vol. 11, no. 3, pp. 339–352, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. M. E. Achhab, B. Aylaj, and M. Laabissi, “Equilibrium profiles for a class of tubular reactor nonlinear models,” in Proceedings of the 13th Mediteranean Conference on Control and Automation (MED '05), Limassol, Cyprus, June 2005.