Existence of Optimal Control for Dirichlet Boundary Optimization in a Phase Field Problem

Abstract Phase field modeling finds utility in various areas. In optimization theory particular, the distributed control and Neumann boundary of phase models have been investigated thoroughly. Dirichlet parabolic equations is commonly addressed using very weak formulation or an approximation by Robin conditions. this paper, for a model with non-singular potential lift technique. The corresponding analyzed. Energy estimates problem-specific embedding results are provided, leading to existence uniqueness solution state equation. These together show that mapping well defined bounded. Based on preceding findings, problem shown solution.