发汗控制第三边值问题解的稳定性

本文研究文献［１］导出的一类活动边界域上分布参数非线性控制系统，其背景是热防护中的发汗冷却系统。这类系统有第三类边界条件：活动的外边界。在域内还可以出现活动的弱间断面，文献［１］从计算机仿真证明了一维系统的适定性、稳定性、可测性和可控性，文献［２］、［３］从理论上证明了第二类边界条件下系统的解的存在性、唯一性和稳定性。本文证明了第三类边界条件下系统解的存在性、唯一性以及解的稳定性。

On the Stability of Solution to Transpiration Control Problem with Third Boundary Value Condition

This paper discusses a class of nonlinear distributed parameter control system with free boundary domain which was derived in the literature 1]. Its physical backguround is the transpiration cooling control system of thermal protection. This problem has the third boundary condition. That is, it not only has the moving outer boundary, but also has the free weakly discontinuous plane in the domain. In the literature 1], the author obtained the well-posedness,controllability and observability properties of the one-dimension system by means of the computer simulation. In the literature 2,3], the authors proved the well-posedness of the second boundary volue problems. respectively. In this note, we prove that the solution of the one-dimensional system with the third boundary condition is exists uniquely and stable.