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Zapiski Nauchnykh Seminarov POMI, 2004, Volume 311, Pages 7–39 (Mi znsl786)  
This article is cited in 3 scientific papers (total in 3 papers)

Generalized solutions of nonlinear parabolic systems and vanishing viscosity method

Ya. I. Belopol'skaya

St. Petersburg State University of Architecture and Civil Engineering
Full-text PDF (315 kB) Citations (3)
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Abstract: In this paper we construct stochastic processes associated with nonlinear parablic equations and systems that allow to derive a probabilistic representation of a generalized solution to the Cauchy problem for them. We show also that in some cases the derived representation can be used to construct and investigate a smooth solution to the Cauchy problem for a hyperbolic system within the framework of the vanishing viscosity method.
Received: 25.06.2004
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 133, Issue 3, Pages 1207–1223
DOI: https://doi.org/10.1007/s10958-006-0031-z
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: Ya. I. Belopol'skaya, “Generalized solutions of nonlinear parabolic systems and vanishing viscosity method”, Probability and statistics. Part 7, Zap. Nauchn. Sem. POMI, 311, POMI, St. Petersburg, 2004, 7–39; J. Math. Sci. (N. Y.), 133:3 (2006), 1207–1223
Citation in format AMSBIB
\Bibitem{Bel04}
\by Ya.~I.~Belopol'skaya
\paper Generalized solutions of nonlinear parabolic systems and vanishing viscosity method
\inbook Probability and statistics. Part~7
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 311
\pages 7--39
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl786}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2092198}
\zmath{https://zbmath.org/?q=an:1083.35043}
\elib{https://elibrary.ru/item.asp?id=9129757}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 133
\issue 3
\pages 1207--1223
\crossref{https://doi.org/10.1007/s10958-006-0031-z}
\elib{https://elibrary.ru/item.asp?id=13522849}
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  • https://www.mathnet.ru/eng/znsl/v311/p7
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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