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Original Articles

Detection of pollution terms in nonlinear second order wave systems

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Pages 13-20 | Received 13 Nov 2016, Accepted 06 Apr 2017, Published online: 04 May 2017

References

  • Lions JL. Sentinelles pour les systèmes distribués à données incomplètes [Sentinels for distributed systems of incomplete data]. Paris: Masson; 1992.
  • Nazemi AR, Effati S. Time optimal control problem of the wave equation. Adv Model Optim. 2010;12(3):363–382.
  • Omrane A. Some aspects of the sentinel method for pollution problems. Air quality – monitoring and modeling. In Kumar S, editor. InTech, Chap 92012, p. 185–204. ISBN 978-953-51-0161-1. DOI:10.5772/33173
  • Miloudi Y, Nakoulima O. Omrane A. A method for detecting pollution in dissipative systems with incomplete data, ESAIM: Proc. 2007;17:67–79.
  • Miloudi Y, Nakoulima O, Omrane A. On the instantaneous sentinels in pollution problems of incomplete data. Inverse Prob Sci Eng. 2009;17(4):451–459.
  • Fursikov A, Imanuvilov OYu. Controllability of evolution equations. Lecture notes: Research institute of mathematics, Seoul National University, Korea; 1996.
  • Lions JL. Contrôlabilité exacte, stabilisation et perturbations des systèmes distribués [Exact controllability, stabilization and perturbations of distributed systems]. Vol. 1. Paris: Masson; 1988. (Contrôlabilité exacte).
  • Bardos C, Lebeau G, Rauch J. Sharp sufficient conditions for the observation, control and stabilization of wave from the boundary. SIAM J Optim Control. 1992;305:1024–1065.
  • Ainseba B-E, Kernevez J-P, Luce R. Identification de paramètres dans des problèmes non linéaires à données incomplètes. M2AN Math Model Numer Anal [Identification of parameters in nonlinear problems of incomplete data]. 1994;28(3):313–328.
  • Dehman B, Lebeau G, Zuazua E. Stabilization and control for the subcritical semilinear wave equation. Ann l’Ecole Normale Supérieure Paris. 2003;36(4):525–551.
  • Gérard P. Microlocal defect measures. Commun Partial Differ Equ. 1991;16:1761–1794.
  • Ruiz A. Unique continuation for weak solutions of the wave equation plus a potential. J Math Pures Appl. 1992;71:455–467.
  • Tataru D. The Xθs spaces and unique continuation for solutions to the semilinear wave equation. Commun Partial Differ Equ. 1996;21(5 & 6):841–887.
  • Dehman B, Omrane A. On the controllability under constraints on the control of hyperbolic equations. Appl Math E-Notes. 2010;10:36–39.

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