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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 442, Pages 18–47 (Mi znsl6242)  
This article is cited in 1 scientific paper (total in 1 paper)

Probabilistic representations and numerical algorithms to construct classical and viscosity solutions of the Cauchy problem for systems of quasilinear parabolic equations

Ya. I. Belopolskaya, E. I. Nemchenko

St. Petersburg State University of Architecture and Civil Engineering, St. Petersburg, Russia
Full-text PDF (324 kB) Citations (1)
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Abstract: We propose two approaches that allow to construct probabilistic representationы of classical and viscosity solutions of the Cauchy problem for systemы of quasilinear parabolic equations. Based on this representations we develop two numerical algorithms to construct the required solutions.
Key words and phrases: stochastic differential equations, systems of quasilinear parabolic equations, classical and viscosity solutions of the Cauchy problem.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-01453
Received: 12.11.2015
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 225, Issue 5, Pages 733–750
DOI: https://doi.org/10.1007/s10958-017-3490-5
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: Ya. I. Belopolskaya, E. I. Nemchenko, “Probabilistic representations and numerical algorithms to construct classical and viscosity solutions of the Cauchy problem for systems of quasilinear parabolic equations”, Probability and statistics. Part 23, Zap. Nauchn. Sem. POMI, 442, POMI, St. Petersburg, 2015, 18–47; J. Math. Sci. (N. Y.), 225:5 (2017), 733–750
Citation in format AMSBIB
\Bibitem{BelNem15}
\by Ya.~I.~Belopolskaya, E.~I.~Nemchenko
\paper Probabilistic representations and numerical algorithms to construct classical and viscosity solutions of the Cauchy problem for systems of quasilinear parabolic equations
\inbook Probability and statistics. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 442
\pages 18--47
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6242}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3506843}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 225
\issue 5
\pages 733--750
\crossref{https://doi.org/10.1007/s10958-017-3490-5}
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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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