DISTRIBUTED ROBUST CONTROL OF KELLER-SEGEL EQUATIONS

  • RYU, SANG-UK (Department of Mathematics Cheju National University) ;
  • YUN, YONG-SIK (Department of Mathematics Cheju National University)
  • Received : 2004.08.10
  • Accepted : 2004.10.08
  • Published : 2004.12.25

Abstract

We are concerned with the robust control problem for the Keller-Segel equations with the distributed control and disturbance. We consider the present problem as a differential game finding the best control which takes into account the worst disturbance. We prove the existence of solutions and the optimality conditions to a corresponding problem.

Keywords

Keller-Segel equations;Distributed robust control;Existence;Optimality conditions

References

  1. J. Math. Anal. Appl. v.164 On the optimal control of strongly nonlinear evolution equations Papageorgiou, N.S.
  2. J. Math. Anal. Appl. v.256 Optimal control of Keller-Segel equations Ryu, S.U.;Yagi, A.
  3. Interpolation theory, function spaces, differential operators Triebel, H.
  4. Analysis and Control of Nonlinear Infinite Dimensional Systems Barbu, V.
  5. Physica D v.138 A general framework for robust control in fluid mechanics Bewley, T.R.;Temam, R.;Ziane, M.
  6. Proc. Roy. Soc. Edinburgh Sect. v.125 Optimal control of quasilinear parabolic equations Casas, E.;Fernandez, L.A.;Yong, J.
  7. Mathematical Analysis and Numerical Methods for Science and Technology 5 Dautray, R.;Lions, J.L.
  8. Journal of theoritical biology v.26 Initiation of slime mold aggregation viewed as an instability Keller, K.L.;Segel, L.A.
  9. Optimal Control of Distributed Parameter Systems Ahmed, N.U.;Teo, K.L.
  10. Optimal Control of Systems Governed by Partial Differential Equations Lions, J.L.