East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

OPTIMAL CONTROL FOR THE FOREST KINEMATIC MODEL

  • Ryu, Sang-Uk (Department of Mathematics, Jeju National University)
  • Received : 2015.04.16
  • Accepted : 2015.05.11
  • Published : 2015.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

This paper is concerned with the optimal control for the forest kinematic model. That is, we show the exiatence of the strong solution for the forest kinematic model and then show the existence of the optimal control.

Keywords

References

  1. M. Ya. Antonovsky, E.A. Aponina, Yu. A. Kuznetsov, Spatial-temporal structure of mixed-age forest boundary: The simplest mathematical model, WP-89-54. Laxenburg, Austria: International Institute for Applied Systems Analysis 1989.
  2. M. Ya. Antonovsky, E. A Aponina, Yu. A. Kuznetsov, On the stability analysis of the standing forest boundary, WP-91-010. Laxenburg, Austria: International Institute for Applied Systems Analysis 1991.
  3. N. C. Apreutesei, An optimal control prolem for a pest, predator, and plant system, Nonlinear Anal. RWA 13 (2012), 1391-1400. https://doi.org/10.1016/j.nonrwa.2011.11.004
  4. N. Apreutesei, G. Dimitriu and R. Strugariu, An optimal control prolem for a two-prey and one-predator model with diffusion, Comput. Math. Appl. 67 (2014), 2127-2143. https://doi.org/10.1016/j.camwa.2014.02.020
  5. V. Barbu, Mathematical Methods in Optimization of Differential Systems, Kluwer Academic Publishers, Dordrecht, 1994.
  6. A.J.V. Brandao, E. Fernandez-Cara, P.M.D. Magalhaes, M.A. Rojas-Medar, Theoretical analysis and control results for the FitzHugh-Nagumo equation, Electron. J. Differential Equations, 2008 (2008), no. 164, 1-20.
  7. L. Zhang and B. Liu, Optimal control prolem for an ecosystem with two competing preys and one predator, J. Math. Anal. Appl. 424 (2015), 201-220. https://doi.org/10.1016/j.jmaa.2014.10.093
  8. 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
  9. J. Simon, Compact sets in the space $L^p$(0, T; B), Ann. Mat. Pura Appl. 146 (1987), 65-96.
  10. A. Yagi, Abstract parabolic evolution equations and their applications, Springer-Verlag, Berlin, 2010.