Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 237, pp. 1-18.

Title: Optimal control applied to native-invasive species
      competition via a PDE model
        
Authors: Wandi Ding (Middle Tennessee State Univ., Murfreesboro, TN, USA)
         Volodymyr Hrynkiv (Univ. of Houston - Downtown, Houston, TX, USA)
	 Xiaoyu Mu (Univ. of Tennessee, Knoxville, TN, USA)

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.