Optimal Control of Singular Parabolic PDEs Modeling Multiphase Stefan-type Free Boundary Problems

Abstract

Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control problems is introduced via finite differences. Existence of the optimal control and the convergence of the sequence of discrete optimal control problems both with respect to functional and control is proved. In particular, convergence of the method of finite differences, and existence, uniqueness and stability estimations are established for the singular PDE problem under minimal regularity assumptions on the coefficients.

Discretization and Convergence of the EIT Optimal Control Problem in 2D and 3D Domains

“…Next, we recall the necessary and sufficient condition for the convergence of the discrete optimal control problems E h , which is the suitable criteria to employ for the proof of method of finite differences for the optimal control problems with distributed parameters ([1]- [10]). Lemma 7.…”