DOI QR코드

DOI QR Code

OPTIMALITY CONDITIONS FOR OPTIMAL CONTROL GOVERNED BY BELOUSOV-ZHABOTINSKII REACTION MODEL

  • RYU, SANG-UK (Department of Mathematics Jeju National University)
  • Received : 2015.04.03
  • Published : 2015.06.30

Abstract

This paper is concerned with the optimality conditions for optimal control problem of Belousov-Zhabotinskii reaction model. That is, we obtain the optimality conditions by showing the differentiability of the solution with respect to the control. We also show the uniqueness of the optimal control.

Keywords

Belousov-Zhabotinskii reaction model;optimality conditions;uniqueness

Acknowledgement

Supported by : Jeju National University

References

  1. H. Brezis, Analyse Fonctionnelle, Masson, Paris, 1983.
  2. M. R. Garvie and C. Trenchea, Optimal control of a nutrient-phytoplankton-zooplankton-fish system, SIAM J. Control Optim. 46 (2007), no. 3, 775-791. https://doi.org/10.1137/050645415
  3. K. H. Hoffman and L. Jiang, Optimal control of a phase field model for solidification, Numer. Funct. Anal. Optimiz. 13 (1992), no. 1-2, 11-27. https://doi.org/10.1080/01630569208816458
  4. J. P. Keener and J. J. Tyson, Spiral waves in the Belousov-Zhabotinskii reaction, Phys. D 21 (1986), no. 2-3, 307-324. https://doi.org/10.1016/0167-2789(86)90007-2
  5. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium system From Dissipative Structure to Order through Fluctuations, John Wiley and Sons, New York, 1977.
  6. S.-U. Ryu, Necessary conditions for optimal boundary control problem governed by some chemotaxis equations, East Asian Math. J. 29 (2013), no. 5, 491-501. https://doi.org/10.7858/eamj.2013.033
  7. S.-U. Ryu, Optimal control for Belousov-Zhabotinskii reaction model, East Asian Math. J. 31 (2015), no. 1, 109-117. https://doi.org/10.7858/eamj.2015.011
  8. S.-U. Ryu and A. Yagi, Optimal control of Keller-Segel equations, J. Math. Anal. Appl. 256 (2001), no. 1, 45-66. https://doi.org/10.1006/jmaa.2000.7254
  9. V. K. Vanag and I. R. Epstein, Design and control of patterns in reaction-diffusion systems, Chaos 18 (2008), 026107. https://doi.org/10.1063/1.2900555
  10. A. Yagi, Abstract Parabolic Evolution Equations and Their Applications, Springer-Verlag, Berlin, 2010.
  11. A. Yagi, K. Osaki, and T. Sakurai, Exponential attractors for Belousov-Zhabotinskii reaction model, Discrete Contin. Dyn. Syst. Suppl (2009), 846-856.
  12. V. S. Zykov, G. Bordiougov, H. Brandtstadter, I. Gerdes, and H. Engel, Golbal control of spiral wave dynamics in an excitable domain of circular and elliptical shape, Phys. Rev. Lett. 92 (2004), 018304. https://doi.org/10.1103/PhysRevLett.92.018304

Cited by

  1. OPTIMAL CONTROL FOR SOME REACTION DIFFUSION MODEL vol.32, pp.3, 2016, https://doi.org/10.7858/eamj.2016.029