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Contemporary Mathematics. Fundamental Directions, 2011, Volume 42, Pages 204–210 (Mi cmfd203)  
This article is cited in 1 scientific paper (total in 1 paper)

Method of characteristics for optimal control problems and conservation laws

N. N. Subbotina, E. A. Kolpakova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya str., Yekaterinburg, 620990, Russia
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Abstract: In this paper, notions of global generalized solutions of Cauchy problems for the Hamilton–Jacobi–Bellman equation and for a quasilinear equation (a conservation law) are introduced in terms of characteristics of the Hamilton–Jacobi equation. Theorems on the existence and uniqueness of generalized solutions are proved. Representative formulas for generalized solutions are obtained and a relation between generalized solutions of the mentioned problems is justified. These results tie nonlinear scalar optimal control problems and one-dimensional stationary conservation laws.
English version:
Journal of Mathematical Sciences, 2014, Volume 199, Issue 5, Pages 588–595
DOI: https://doi.org/10.1007/s10958-014-1886-z
Bibliographic databases:
Document Type: Article
UDC: 519.857
Language: Russian
Citation: N. N. Subbotina, E. A. Kolpakova, “Method of characteristics for optimal control problems and conservation laws”, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), CMFD, 42, PFUR, M., 2011, 204–210; Journal of Mathematical Sciences, 199:5 (2014), 588–595
Citation in format AMSBIB
\Bibitem{SubKol11}
\by N.~N.~Subbotina, E.~A.~Kolpakova
\paper Method of characteristics for optimal control problems and conservation laws
\inbook Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3--7, 2009)
\serial CMFD
\yr 2011
\vol 42
\pages 204--210
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd203}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3013841}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 199
\issue 5
\pages 588--595
\crossref{https://doi.org/10.1007/s10958-014-1886-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902766720}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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