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Optimal control of advective direction in reaction-diffusion population models

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  • 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.
    Mathematics Subject Classification: Primary: 35K57, 49K20; Secondary: 92D95.


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