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<p>In this paper, a new nonlinear reaction-diffusion food chain model is proposed and an optimal control problem is established to maximize the total number of all populations in the model and minimize the total control cost as much as possible. As the basis of theoretical analysis, the well-posedness and some estimates of the positive strong solution to the state system and the existence of the optimal pair are proven in a Hilbert space by employing the methods of functional analysis. Then, the first-order necessary optimality condition satisfied by the optimal control is obtained by using convex perturbation theory and duality techniques. Finally, a specific example and its numerical simulations are provided in order to confirm the theoretical results.</p>

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An optimal control problem of a food chain model governed by reaction-diffusion equations

  • 期刊论文

  • 发表日期：

    2026年5月9日

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  • Qixuan Liu,
  • Huili Xiang,
  • Min Zhou

摘要

In this paper, a new nonlinear reaction-diffusion food chain model is proposed and an optimal control problem is established to maximize the total number of all populations in the model and minimize the total control cost as much as possible. As the basis of theoretical analysis, the well-posedness and some estimates of the positive strong solution to the state system and the existence of the optimal pair are proven in a Hilbert space by employing the methods of functional analysis. Then, the first-order necessary optimality condition satisfied by the optimal control is obtained by using convex perturbation theory and duality techniques. Finally, a specific example and its numerical simulations are provided in order to confirm the theoretical results.