Honam Mathematical Journal (호남수학학술지)

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BOUNDARY CONTROL OF CHEMOTAXIS REACTION DIFFUSION SYSTEM

  • Ryu, Sang-Uk (Department of Mathematics, Cheju National University)
  • Received : 2008.05.21
  • Accepted : 2008.09.04
  • Published : 2008.09.25
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Abstract

This paper is concerned with the boundary control of the chemotaxis reaction diffusion system. That is, we show the existence of the solution for the chemotaxis system with the boundary control and the existence of the optimal boundary control.

Keywords

References

  1. R. A. Adams, Soboleb spaces, Academic Press, New York, 1975.
  2. E. F. Keller and L. A. Segel, Initiation of slime mold aggregation viewed as an instability, J. theor. Biol. 26(1970), 399-415. https://doi.org/10.1016/0022-5193(70)90092-5
  3. D. Lebiedz and H. Maurer, External optimal control of self-organization dynamics in a chemotaxis reaction diffusion system, lEE Syst. Biol. 2(2004), 222-229.
  4. J. L. Lions, Quelques Methodes de Resolution des Problemes aux Limites Non Lineaires, Dunford/Gauthier-Villars, Paris, 1969.
  5. K. Osaki and A. Yagi, Finite dimensional attractor for one-dimensional Keller-Segel equations, Funkcial Ekvac. 44(2001), 441-469.
  6. S.-U. Ryu and A. Vagi, Optimal control of Keller-Segel equations, J. Math. Anal. Appl. 256(2001), 45-66. https://doi.org/10.1006/jmaa.2000.7254
  7. H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam 1978.

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  2. NECESSARY CONDITIONS FOR OPTIMAL BOUNDARY CONTROL PROBLEM GOVERNED BY SOME CHEMOTAXIS EQUATIONS vol.29, pp.5, 2013, https://doi.org/10.7858/eamj.2013.033