A Product Formula Approach to a Nonhomogeneous Boundary Optimal Control Problem Governed by Nonlinear Phase‐field Transition System

The paper establishes existence, uniqueness and regularity for the solution of a phase‐field transition system with non‐homogeneous Cauchy‐Neumann boundary conditions. Moreover, some estimates for the solution are given. The non‐linear parabolic problem considered here can be used to modeling the solidification (liquidification) process to a matter. The non‐homogeneous boundary conditions (depending both on time and space variables) can be understood as a boundary control.