Rigorous homogenisation of an optimal control problem for multispecies diffusion-reaction equations
• Arghya Kundu,
• Hari Mahato
Arghya Kundu
IIT Kharagpur

Corresponding Author:arghyakundu5@gmail.com

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Hari Mahato
IIT Kharagpur
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## Abstract

We study an optimal control problem governed by diffusion-reaction equations in a periodic porous medium (bounded domain). Our control problem is equivalent to a convex minimization problem. We take a $L^2$-cost functional and pose controls on the mobile species present in the pore part of the domain. One of the main aims here is to characterize a given control to be an optimal control for the microscopic problem. We obtain the existence of solution of the control problem and analyse a relation between optimal control and its adjoint state. Then, we do the homogenization of the optimal control problem (diffusion-reaction model with cost functional) by a formal asymptotic analysis and then via rigorous two-scale convergence and periodic unfolding method.