Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ROBUST CONTROL FOR A PARABOLIC SYSTEM OF CHEMOTAXIS

  • Ryu, Sang-Uk (Department of Mathematics, Cheju National University) ;
  • Yun, Yong-Sik (Department of Mathematics, Cheju National University)
  • Received : 2008.01.18
  • Accepted : 2008.04.10
  • Published : 2008.06.25
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Abstract

We are concerned with the robust control problem for the chemotaxis equations with predator-prey dynamics. That is, we present the existence and uniqueness of the solution. We also show the existence of the robust control and deduce the corresponding optimality conditions.

Keywords

References

  1. V. Barbu and T. Precupanu, Convexity and Optimization in Banach spaces, Reidel, Dordrecht, 1986.
  2. A. Belmiloudi, Robust and optimal control problems to a phase-field model for the solidification of a binary alloy with a constant temperature, Journal of Dynamical and Control systems 10(4)(2004), 453-499. https://doi.org/10.1023/B:JODS.0000045361.82698.7f
  3. T. R. Bewley and R. Temam, and M. Ziane, A general framework for robust control in fluid mechanics, Physica D 138(2000), 360-392. https://doi.org/10.1016/S0167-2789(99)00206-7
  4. E. O. Budrene and H. C. Berg, Complex patterns formed by motile cells of Escherichia coli, Nature 349(1991), 630-633. https://doi.org/10.1038/349630a0
  5. C. Hu and R. Temam, Robust control of Kuramoto-Sivashinsky equation, Dynam. Contin. Discrete Impuls. Systems 8(2001), 315-338.
  6. H. Kawasaki, A. Mochizuki and N. Shigesada, Mathematical model for patterns by a colony of bacteria (in Japanese), Keisoku to Seigyo 34(1995), 812-817.
  7. J. L. Lions, Non-homogeneous boundary value problems and applications, Vol. 1, Springer-Verlag, Berlin, 1972.
  8. H. Mori, Global existence of the cauchy problem for a chemotatic system with predator-prey dynamics, Hiroshima Math. J. 36(2006), 77-111.
  9. K. Osaki, T. Tsujikawa, A. Yagi and M. Mimura, Exponential attractor for a chemotaxis-growth system of equations, Nonlinear Analysis 51(1)(2002), 119-144. https://doi.org/10.1016/S0362-546X(01)00815-X
  10. S.-U. Ryu and A. Yagi, Optimal control of Keller-Segel equations, J. Math. Anal. Appl. 256(2001), 45-66. https://doi.org/10.1006/jmaa.2000.7254
  11. S.-U. Ryu and Y.-S. Yun, Distributed robust control of Keller-Segel equations, Honam Mathematical J. 26(4)(2005), 423-439.
  12. H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam, 1978.
  13. E. Zeidler, Nonlinear functional analysis and its applications. II/B. Nonlinear monotone operator, Springer-Verlag, Berlin, 1990.