New unexpected limit operators for homogenizing optimal control parabolic problems with dynamic reaction flow on the boundary of critically scaled particles

TL;DR

This paper investigates the homogenization of an optimal control problem involving a parabolic PDE with dynamic boundary conditions, revealing new limit operators and unexpected terms arising at critical scales.

Contribution

It introduces novel limit operators for homogenizing parabolic control problems with dynamic boundary conditions at critical scales, highlighting unexpected terms.

Findings

New limit operators identified for homogenization

Unexpected terms appear at critical scaling

Enhanced understanding of boundary control problems

Abstract

We pass to the limit in the homogenization of an optimal control problem associated with a parabolic equation with a dynamic boundary condition. New unexpected terms appear due to the critical scale.