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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 454, Pages 5–42 (Mi znsl6382)  
This article is cited in 5 scientific papers (total in 5 papers)

Probabilistic models of parabolic conservation and balance laws and systems with switching regimes

Ya. I. Belopolskaya

St. Petersburg State University of Architecture and Civil Engineering, St. Petersburg, Russia
Full-text PDF (319 kB) Citations (5)
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Abstract: We construct a probabilistic representation of the Cauchy problem classical solution for systems of semilinear parabolic equations such that their second order terms enter in a diagonal way with different coefficients while lower order term enter in nondiagonal way. Systems of this kind arise as mathematical models of parabolic conservation and balance laws and as mathematical models of dynamical systems with switching regimes.
Key words and phrases: stochastic differential equations, Markov chains, systems of semilinear parabolic equations, classical solutions of the Cauchy problem.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-01453
Received: 14.11.2016
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 229, Issue 6, Pages 601–625
DOI: https://doi.org/10.1007/s10958-018-3701-8
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: Ya. I. Belopolskaya, “Probabilistic models of parabolic conservation and balance laws and systems with switching regimes”, Probability and statistics. Part 24, Zap. Nauchn. Sem. POMI, 454, POMI, St. Petersburg, 2016, 5–42; J. Math. Sci. (N. Y.), 229:6 (2018), 601–625
Citation in format AMSBIB
\Bibitem{Bel16}
\by Ya.~I.~Belopolskaya
\paper Probabilistic models of parabolic conservation and balance laws and systems with switching regimes
\inbook Probability and statistics. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 454
\pages 5--42
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6382}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3602399}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 229
\issue 6
\pages 601--625
\crossref{https://doi.org/10.1007/s10958-018-3701-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042230114}
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  • https://www.mathnet.ru/eng/znsl/v454/p5
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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