On the Conservation Laws in the Optimal Control Problem for Laminar Boundary Layer of Electroconductive Gas
Author(s):
Natalya Grigorievna Bilchenko
Candidate of Science in Physics and Mathematics
Researcher of Research Laboratory #16,
Department of Heat Engineering and Power Engineering Machinery,
Kazan National Research Technical University (KNRTU-KAI)
named after A. N. Tupolev.
bilchnat@gmail.com
Abstract:
The problems of mathematical modeling of optimal heat protection
of permeable surfaces of hypersonic aircraft in ionized gas are considered.
The group theory approach to the optimization
of systems with distributed parameters is applied.
The table of infinitesimal operators of a Lie group admissible
by a system of nonlinear differential equations of parabolic type is modified.
Conservation laws on all operators of the admissible group are constructed.
A theorem on the existence of the first integral of the optimal problem is proved.
Keywords
- conservation law
- first integral
- heat and mass transfer
- hypersonic flows
- infinitesimal operator
- ionization
- laminar boundary layer
- Lie group
- optimal control
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