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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/cmfd203
https://www.mathnet.ru/eng/cmfd/v42/p204
This publication is cited in the following 1 articles:
Oleg Malafeyev, Konstantin Farvazov, Olga Zenovich, Irina Zaitseva, Konstantin Kostyukov, Tatiana Svechinskaya, AIP Conference Proceedings, 1952, 2018, 020066
Citation in format AMSBIB
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