An optimal control problem for diffusion–precipitation model

Article type: Research Article

Authors: Kundu, A. | Mahato, H.S.^{; *}

Affiliations: Department of Mathematics, IIT Kharagpur, India

Correspondence: [*] Corresponding author. E-mail: hsmahato@maths.iitkgp.ac.in.

Abstract: We present an optimal control problem associated to a chemical transportation phenomena in a periodic porous medium. Posing controls on the porous part of the medium (distributed control), we set up a convex minimization problem. The main objective of this article is to characterize an arbitrary control to be an optimal control. We establish a relation between the optimal control and the corresponding adjoint state. At first, we analyse the microscopic description of the controlled system, then we homogenised the system by rigorous two-scale convergence method and periodic unfolding method.

Keywords: Diffusion–reaction–precipitation equations, optimal control problem, homogenisation, periodic porous medium, existence of solution, asymptotic expansion, two-scale convergence

DOI: 10.3233/ASY-241905

Journal: Asymptotic Analysis, vol. 139, no. 3-4, pp. 183-215, 2024