Wandi Ding, Volodymyr Hrynkiv, Xiaoyu Mu
Abstract:
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 |
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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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