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Evolution Equations and Control Theory (EECT)
 

Optimal control of advective direction in reaction-diffusion population models

Pages: 81 - 107, Volume 1, Issue 1, June 2012      doi:10.3934/eect.2012.1.81

 
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Heather Finotti - 1400 Kenesaw Ave, 31F, Knoxville, TN 37132, United States (email)
Suzanne Lenhart - Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, United States (email)
Tuoc Van Phan - Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, United States (email)

Abstract: We investigate optimal control of the advective coefficient in a class of parabolic partial differential equations, modeling a population with nonlinear growth. This work is motivated by the question: Does movement toward a better resource environment benefit a population? Our objective functional is formulated with interpreting "benefit" as the total population size integrated over our finite time interval. Results on existence, uniqueness, and characterization of the optimal control are established. Our numerical illustrations for several growth functions and resource functions indicate that movement along the resource spatial gradient benefits the population, meaning that the optimal control is close to the spatial gradient of the resource function.

Keywords:  Parabolic partial differential equations, optimal control, maximum principle, advective direction, reaction-diffusion, population model.
Mathematics Subject Classification:  Primary: 35K57, 49K20; Secondary: 92D95.

Received: November 2011;      Revised: February 2012;      Available Online: March 2012.

 References