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Trudy Inst. Mat. i Mekh. UrO RAN, 2007, Volume 13, Number 2, Pages 135–144 (Mi timm96)  

This article is cited in 4 scientific papers (total in 4 papers)

On viscosity solution of functional Hamilton–Jacobi type equations for hereditary systems

N. Yu. Lukoyanov


Abstract: The paper is devoted to the development of the viscosity approach to the generalized solution of functional Hamilton–Jacobi type equations with coinvariant derivatives and a nonanticipatory Hamiltonian. These equations are naturally connected to problems of dynamical optimization of hereditary systems and, as compared with classical Hamilton–Jacobi equations, possess a number of additional peculiarities stipulated by the aftereffect. The definition of a viscosity solution that takes the above peculiarities into account is given. The consistency of this definition with the notion of a classical solution and with the minimax approach to the generalized solution is substantiated. The existence and uniqueness theorems are proved.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2007, 259, suppl. 2, S190–S200

UDC: 517.977
Received: 04.05.2007

Citation: N. Yu. Lukoyanov, “On viscosity solution of functional Hamilton–Jacobi type equations for hereditary systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 2, 2007, 135–144; Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S190–S200

Citation in format AMSBIB
\Bibitem{Luk07}
\by N.~Yu.~Lukoyanov
\paper On viscosity solution of functional Hamilton--Jacobi type equations for hereditary systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2007
\vol 13
\issue 2
\pages 135--144
\mathnet{http://mi.mathnet.ru/timm96}
\elib{http://elibrary.ru/item.asp?id=12040776}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2007
\vol 259
\issue , suppl. 2
\pages S190--S200
\crossref{https://doi.org/10.1134/S0081543807060132}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38949173294}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. Yu. Lukoyanov, “Minimax and viscosity solutions in optimization problems for hereditary systems”, Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S214–S225  mathnet  crossref  elib
    2. Vostrikov I.V., “O metode dinamicheskogo programmirovaniya dlya lineinykh upravlyaemykh sistem s zapazdyvaniem”, Vestnik moskovskogo universiteta. seriya 15: vychislitelnaya matematika i kibernetika, 2 (2012), 15a–21  mathscinet  elib
    3. Ren Zh., Touzi N., Zhang J., “Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs”, SIAM J. Math. Anal., 49:5 (2017), 4093–4116  crossref  mathscinet  zmath  isi  scopus
    4. Qiu J., Wei W., “Uniqueness of Viscosity Solutions of Stochastic Hamilton-Jacobi Equations”, Acta Math. Sci., 39:3, SI (2019), 857–873  crossref  isi
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