Electron. J. Diff. Equ., Vol. 2012 (2012), No. 237, pp. 1-18.

Optimal control applied to native-invasive species competition via a PDE model

Wandi Ding, Volodymyr Hrynkiv, Xiaoyu Mu

We consider an optimal control problem of a system of parabolic partial differential equations modelling the competition between an invasive and a native species. The motivating example is cottonwood-salt cedar competition, where the effect of disturbance in the system (such as flooding) is taken to be a control variable. Flooding being detrimental at low and high levels, and advantageous at medium levels led us to consider the quadratic growth function of the control. The objective is to maximize the native species and minimize the invasive species while minimizing the cost of implementing the control. An existence result for an optimal control is given. Numerical examples are presented to illustrate the results.

Submitted September 5, 2012. Published December 26, 2012.
Math Subject Classifications: 49J20, 34K35, 92D25.
Key Words: Optimal control; partial differential equations; native-invasive species; salt cedar; cottonwood; spatial models.

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Wandi Ding
Department of Mathematical Sciences and Computational Science Program
Middle Tennessee State University
Murfreesboro, TN 37132, USA
email: wandi.ding@mtsu.edu
Volodymyr Hrynkiv
Department of Computer and Mathematical Sciences
University of Houston - Downtown
Houston, TX 77002, USA
email: HrynkivV@uhd.edu
  Xiaoyu Mu
Department of Mathematics
University of Tennessee
Knoxville, TN 37996-1320, USA
email: xiaoyumoon@gmail.com

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