摘要
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.
在不计热膨胀效应的情形下，简单地建立了一个烧蚀过程的发汗冷却控制的分布参数模型．对于固定的控制分布，证明了正解的存在唯一性，导出了烧蚀过程在有限时间结束的条件．最后，证明了临界发汗量的存在性．
基金
国家自然科学基金
