Optimal control with phase constraints for a quasilinear endovenous laser ablation model

An optimal control problem for quasilinear equations of radiative-conductive heat transfer simulating the process of endovenous laser ablation in a bounded domain with the reflecting boundary is studied. In a given subdomain, it is required to provide a given temperature distribution, while the temperature in another given subdomain cannot exceed a critical value. On the basis of estimates of the solution of the controlled system, the solvability of the control problem is proved. An algorithm for solving the optimal control problem by minimizing the objective functional with a penalty is proposed. The efficiency of the algorithm is illustrated by a numerical example.