A Population Harvesting Model with Time and Size Competition Dependence Function

B. Ainseba (), L. Louison () and A. Omrane ()
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B. Ainseba: Université de Bordeaux
L. Louison: Université de Guyane
A. Omrane: Université de Guyane

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 2, No 11, 647-665

Abstract: Abstract We consider a nonlinear model describing a forest harvesting of a size-structured trees population with intra-specific competition, where the population compete with trees of bigger size. Using a fixed point argument, we prove the existence of a unique solution to the problem. We also prove the existence of an optimal control where the objective functional includes the benefits from timber production. Then, we give the necessary condition of optimality for the optimal control and give its characterization as well.

Keywords: Size-structured population; Competition function; Timber production; Fixed point theory; Maximum principle; Bang–bang optimal control; 35L65; 92D25; 65M06 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02102-2

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