2023/09/16 by Gianni Gilardi, Gilardi, Gianni, Elisabetta Rocca +3
Computer Science · Materials Science · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2309.09053
openalex publication_date 2023/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider a nonlinear system of PDEs coupling the viscous Cahn-Hilliard-Oono equation with dynamic boundary conditions enjoying a similar structure on the boundary. After proving well-posedness of the corresponding initial boundary value problem, we study an associated optimal control problem related to a tracking-type cost functional, proving first-order necessary conditions of optimality. The controls enter the system in the form of a distributed and a boundary source. We can account for general potentials in the bulk and in the boundary part under the common assumption that the boundary potential is dominant with respect to the bulk one. For example, the regular quartic potential as well as the logarithmic potential can be considered in our analysis.