On the convergence of controls and cost functionals in some optimal control heterogeneous problems when the homogenization process gives rise to some strange terms

We consider the convergence of solutions and cost functional in some optimal control problems arising in the study of the adsorption chemical phenomenon in which some microscopic reactant particles are placed over an internal manifold gamma of the chemical reactor Omega. The chemical reaction is given by some Robin-type boundary condition on the boundary of the periodic set of particles. We consider the special case in which there is a critical relation between the coefficient of the reaction, the size of the particles and the dimension of the space. This gives rise to a strange term, which is not occurring for other scales, and thus the limit cost functional must be suitably defined. In a last section, we use this type of technique to prove a similar energy convergence result (improving the H-0(1) (Omega)-weak convergence) for the problem without control for the critical scale case. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study focuses on the convergence of solutions and cost functional in optimal control problems related to the adsorption chemical phenomenon. The critical relationship between reaction coefficients, particle sizes, and spatial dimensions is analyzed, leading to the need for a suitably defined limit cost functional for the problem. The study also demonstrates the improvement of energy convergence results in the critical scale case without control.