Optimal control of endovenous laser ablation

On the base of an initial-boundary value problem for the model of radiation-conductive heat transfer, the thermal processes that occur during endovenous laser ablation are studied. An optimal control problem is posed, which consists in approximating the solution of the initial-boundary value problem to a given temperature profile at a certain point of the model domain. The source powers going on radiation and heating the carbonized tip of the optical fiber are taken as control. An iterative algorithm for solving the problem is proposed and numerically implemented.