An instantaneous semi-Lagrangian approach for boundary control of a melting problem

In this paper, a sub-optimal boundary control strategy for free problem is investigated. The model described by non-smooth convection-diffusion equation. addressed an instantaneous based on the characteristics method. resulting time independent problems are formulated as function space optimization with complementarity constraints. At each step, existence of optimal solution proved and first-order optimality conditions regular Lagrange multipliers derived penalized-regularized version. performance overall approach illustrated numerical examples.