A Product Formula Approach to a Nonhomogeneous Boundary Optimal Control Problem Governed by Nonlinear Phase-field Transition System Part I: A Phase-field Model

摘要

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.