Modelling and Solution of a Ablation-Transpiration Cooling Control Systems

A controlled model of thermal shield of ablation with trapspiration cooling is develoed. The existence and uniqueness of the classical solution can be obtained by Friedman and Jiang's methods. The positivity of the solution is proved and the conditions for the coolant flux under which the abladtion process will complete in finite time are also determined. Finally, we show the existence of critical coolant flux beyond which the ablation material begin melting.