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Zap. Nauchn. Sem. POMI, 2016, Volume 454, Pages 220–237 (Mi znsl6395)  

This article is cited in 2 scientific papers (total in 2 papers)

A probabilistic representation of the Cauchy problem solution for an evolution equation with the differential operator of the order greater than 2

M. V. Platonova

Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia

Abstract: Let $m$ be a positive integer. We construct a probabilistic representation of the Cauchy problem solution for the high-order heat-type equation $\frac{\partial u}{\partial t}=c_m\frac{\partial^mu}{\partial^mx}$.

Key words and phrases: evolution equation, Cauchy problem, Poisson random measure.

Funding Agency Grant Number
Russian Science Foundation 14-21-00035


Full text: PDF file (226 kB)
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English version:
Journal of Mathematical Sciences (New York), 2018, 229:6, 744–755

Bibliographic databases:

UDC: 519.2
Received: 24.10.2016

Citation: M. V. Platonova, “A probabilistic representation of the Cauchy problem solution for an evolution equation with the differential operator of the order greater than 2”, Probability and statistics. Part 24, Zap. Nauchn. Sem. POMI, 454, POMI, St. Petersburg, 2016, 220–237; J. Math. Sci. (N. Y.), 229:6 (2018), 744–755

Citation in format AMSBIB
\Bibitem{Pla16}
\by M.~V.~Platonova
\paper A probabilistic representation of the Cauchy problem solution for an evolution equation with the differential operator of the order greater than~2
\inbook Probability and statistics. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 454
\pages 220--237
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6395}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3602412}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 229
\issue 6
\pages 744--755
\crossref{https://doi.org/10.1007/s10958-018-3714-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042210000}


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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. I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Probabilistic Approximation of the Evolution Operator”, Funct. Anal. Appl., 52:2 (2018), 101–112  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. K. Nikolaev, M. V. Platonova, “Neveroyatnostnye analogi protsessa Koshi”, Veroyatnost i statistika. 27, Zap. nauchn. sem. POMI, 474, POMI, SPb., 2018, 183–194  mathnet
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