Optimal control of a diffusion/reaction/switching system

Thomas I. Seidman

doi:10.3934/eect.2013.2.723

Article Contents

2013, Volume 2, Issue 4: 723-731. Doi: 10.3934/eect.2013.2.723

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Optimal control of a diffusion/reaction/switching system

Thomas I. Seidman^1,

1.
Department of Mathematics and Statistics, University of Maryland Baltimore County (UMBC), Baltimore, MD 21250

Received: October 31, 2012

Revised: May 31, 2013

Published: November 2013

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Abstract

We consider an optimal control problem involving the use of bacteria for pollution removal where the model assumes the bacteria switch instantaneously between active and dormant states, determined by threshold sensitivity to the local concentration $v$ of a diffusing critical nutrient; compare [7], [3], [6] in which nutrient transport is convective. It is shown that the direct problem has a solution for each boundary control $ψ = ∂v/∂n$ and that optimal controls exist, minimizing a combination of residual pollutant and aggregated cost of the nutrient.

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Mathematics Subject Classification: Primary: 49J21; Secondary: 34K34, 35K40.

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