Maxi mumprinciple for the optimal control of an ablation-transpiration cooling system with free final time and phase constraints

paper is concerned with an optimal co nt rol problem of an ablation-transpiration cooling control system with Stefan-Sig norini boundary condition.As the continuation of the authors'previous paper,the Dubovits Rii-Milyutin functional approach is again adopted in investigation of t he Pontryagin's maximun principle of the system.The necessary optimality condit ion is presented for the problem with free final horizon and phase constraints.