On a corollary of the noether theorem for the two-dimensional problem of the Mayer type

Abstract

The group-theoretical approach to the construction of differential laws of conservation is considered for two-dimensional Mayer type problems. Approach is based on the use of the Lie-Ovsiannikov theory and the Noether theorem /4,5/ which is the fundamental tool for deriving the laws of conservation for uncontrolled physical processes (see, e.g., /6–9/). Certain classes of optimally controlled processes were earlier considered in /10–12/ from the point of view of the Noether theory. Sufficient conditions of existence of first integrals of two-dimensional variational problems of the Mayer type are obtained. As an example, the problem of heat transfer optimization in the boundary layer of a compressible gas is considered.