Optimal control problem for a nonlinear nonlocal evolution system describing an interacting ternary mixture with an evaporating component: 2D case with bulk evaporation

TL;DR

This paper formulates an optimal control problem for phase separation in polymer solvent mixtures, focusing on solvent evaporation to influence morphology in organic solar cells, and derives optimality conditions.

Contribution

It introduces a new optimal control framework for morphology formation in organic solar cells considering evaporation effects and provides existence and optimality conditions.

Findings

Existence of optimal controls established.

Frechet derivative of control-to-state map analyzed.

First order optimality conditions derived.

Abstract

We present an optimal control problem to guide the selection of morphology classes arising in organic solar cells. The study focuses on phase separation processes in polymer solvent mixtures, with particular attention to solvent evaporation as a mechanism to arrest morphology formation. We establish the existence of optimal controls and analyze the Frechet derivative of the control to state mapping. Finally, we derive the first order necessary optimality condition via the corresponding adjoint system.