Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Advection control in parabolic PDE systems for competitive populations

Pages: 1049 - 1072, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017052

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Kokum R. De Silva - Department of Mathematics, University of Peradeniya, Peradeniya, KY 20400, Sri Lanka (email)
Tuoc V. Phan - Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1320, United States (email)
Suzanne Lenhart - University of Tennessee, Department of Mathematics, 227 Ayres Hall, 1403 Circle Drive, Knoxville, TN 37996-1320, United States (email)

Abstract: This paper investigates the response of two competing species to a given resource using optimal control techniques. We explore the choices of directed movement through controlling the advective coefficients in a system of parabolic partial differential equations. The objective is to maximize the abundance represented by a weighted combination of the two populations while minimizing the `risk' costs caused by the movements.

Keywords:  Optimal control, advection direction, competitive systems, partial differential equations, parabolic system.
Mathematics Subject Classification:  Primary: 49K20, 92B05; Secondary: 35K57.

Received: May 2016;      Revised: December 2016;      Available Online: January 2017.