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<p>We explore an optimal control problem governed by diffusion-reaction equations within a periodic porous medium (bounded). The control problem is equivalent to a convex minimization problem. We employ an <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10883_2025_9746_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^2\)</EquationSource> </InlineEquation>-cost functional and introduce controls (distributed) within the pore part of the domain. The main aim of this article is to characterize a given control to be an optimal control. This analysis leads us to a relation between optimal control and adjoint state. Subsequently, we homogenise the optimal control problem by formal asymptotic expansion method and then via rigorous two-scale convergence and periodic unfolding method.</p>

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Homogenisation of an Optimal Control Problem for Multispecies Diffusion-Reaction Equations

  • 期刊论文

  • 发表日期：

    2025年8月22日

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  • A. Kundu,
  • H. S. Mahato

摘要

We explore an optimal control problem governed by diffusion-reaction equations within a periodic porous medium (bounded). The control problem is equivalent to a convex minimization problem. We employ an \(L^2\) -cost functional and introduce controls (distributed) within the pore part of the domain. The main aim of this article is to characterize a given control to be an optimal control. This analysis leads us to a relation between optimal control and adjoint state. Subsequently, we homogenise the optimal control problem by formal asymptotic expansion method and then via rigorous two-scale convergence and periodic unfolding method.