Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 4, Pages 339-361
doi:10.1155/S1048953392000297

Existence of solution to transpiration control problem

Guanstian Zhu,1 Jingang Wu,2 Benzhon4g Liang,2 Xinhua Ji,3 and Xueshi Yang4

1lnstitute of System Science, Academia Sinica, Beijing, China
2Xinyang Teachers College, Henan, China
3Institute of Mathematics, Academia Sinica, Beijing, China
4P.O. Box 3924, Beijing, China

Received 1 September 1991; Revised 1 June 1992

Copyright © 1992 Guanstian Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Transpiration control can avoid change of the shape of a high-speed vehicle resulting from ablation of the nose, therefore also can avoid the change of the performance of Aerodynamics. Hence it is of practical importance. A set of mathematical equations and their boundary conditions are founded and justified by an example of non-ablation calculation in reference [1]. In [2], the ablation model is studied by the method of finite differences, the applicable margin of the equations is estimated through numerical calculation, and the dynamic responses of control parameters are analyzed numerically. In this paper we prove that the solution to transpiration control problem given in [1] exists uniquely under the assumption that the given conditions (i.e. given functions) are continuous.