Optimal Control of a PDE Model of an Invasive Species in a River

Rebecca Pettit and Suzanne Lenhart
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Rebecca Pettit: Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1320, USA
Suzanne Lenhart: Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1320, USA

Mathematics, 2019, vol. 7, issue 10, 1-17

Abstract: Managing invasive species in rivers can be assisted by appropriate adjustment of flow rates. Using a partial differential equation (PDE) model representing an invasive population in a river, we investigate controlling the water discharge rate as a management strategy. Our goal is to see how controlling the water discharge rate will affect the invasive population, and more specifically how water discharges may force the invasive population downstream. We complete the analysis of a flow control problem, which seeks to minimize the invasive population upstream while minimizing the cost of this management. Using an optimality system, consisting of our population PDE, an adjoint PDE, and corresponding optimal control characterization, we illustrate some numerical simulations in which parameters are varied to determine how far upstream the invasive population reaches. We also change the river’s cross-sectional area to investigate its impact on the optimal control.

Keywords: optimal control; partial differential equation; invasive species in a river (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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