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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2014, Volume 156, Book 4, Pages 5–13 (Mi uzku1275)  
Theory of invariant variational problems and its applications

K. G. Garaev

Kazan State Technical University, Kazan, Russia
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Abstract: A brief review of the works on the modified theory of invariant variational problems and its applications, developed by the author, is presented. The research is based on the infinitesimal Li–Ovsyannikov formalism and E. Noether's fundamental idea of invariant functionals. Theorems on generalized invariance are proved, and the application of the developed theory to the solution of optimal problems of mathematical physics is discussed.
Keywords: Lee group, integral invariant, functional invariance, Noether's generalized theorem, Pontryagin's maximum principle, Bellman's equation.
Received: 18.12.2013
Document Type: Article
UDC: 517.97
Language: Russian
Citation: K. G. Garaev, “Theory of invariant variational problems and its applications”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 156, no. 4, Kazan University, Kazan, 2014, 5–13
Citation in format AMSBIB
\Bibitem{Gar14}
\by K.~G.~Garaev
\paper Theory of invariant variational problems and its applications
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2014
\vol 156
\issue 4
\pages 5--13
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1275}
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