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Teoriya Veroyatnostei i ee Primeneniya, 2004, Volume 49, Issue 4, Pages 625–652
DOI: https://doi.org/10.4213/tvp186 (Mi tvp186) 		 
This article is cited in 3 scientific papers (total in 3 papers)

A probabilistic approach to a solution of nonlinear parabolic equations

Ya. I. Belopol'skaya

St. Petersburg State University of Architecture and Civil Engineering
Full-text PDF (2987 kB) Citations (3)
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DOI: https://doi.org/10.4213/tvp186
Abstract: We construct a probabilistic representation of the Cauchy problem solution for a system of nonlinear parabolic equations and give the conditions which guarantee that this representation can be applied to construct and investigate a solution of the Cauchy problem for a system of nonlinear hyperbolic equations. As an example, we consider the system of gas dynamic equations and its parabolic regularization.
Keywords: diffusion processes, multiplicative operator functionals, systems of nonlinear parabolic and hyperbolic equations, vanishing viscosity methodю.
Received: 25.02.2004
English version:
Theory of Probability and its Applications, 2005, Volume 49, Issue 4, Pages 589–611
DOI: https://doi.org/10.1137/S0040585X97981287
Bibliographic databases:
Language: Russian
Citation: Ya. I. Belopol'skaya, “A probabilistic approach to a solution of nonlinear parabolic equations”, Teor. Veroyatnost. i Primenen., 49:4 (2004), 625–652; Theory Probab. Appl., 49:4 (2005), 589–611
Citation in format AMSBIB
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\by Ya.~I.~Belopol'skaya
\paper A probabilistic approach to a solution of nonlinear parabolic
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\pages 625--652
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\transl
\jour Theory Probab. Appl.
\yr 2005
\vol 49
\issue 4
\pages 589--611
\crossref{https://doi.org/10.1137/S0040585X97981287}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000234407500002}
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  • https://www.mathnet.ru/eng/tvp186
  • https://doi.org/10.4213/tvp186
  • https://www.mathnet.ru/eng/tvp/v49/i4/p625
    • 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
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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