Optimal control problems of phase field system with total variation functional as the interfacial energy (Q1943335)

This paper presents the case of an optimal control problem in one spatial dimension for a phase field system consisting of two parabolic partial differential equations, namely a heat equation and a diffusion one. The element of novelty comes from the fact that the cost functional is both nonlinear and non-smooth, one of the main equation constraints of the optimal control problem having a singularity. The article is well written and presented in a very clear manner. The approach is constructive by considering an approximating system and the results include the thorough argument for the existence of an optimal control and also the derivation of necessary conditions for qualifying optimality.