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Mathematics of the USSR-Sbornik, 1971, Volume 14, Issue 4, Pages 453–469
DOI: https://doi.org/10.1070/SM1971v014n04ABEH002815
(Mi sm3266)
 

This article is cited in 4 scientific papers (total in 4 papers)

On uniqueness classes for degenerating parabolic equations

I. M. Sonin
References:
Abstract: We study the uniqueness classes of a generalized solution of the Cauchy problem
\begin{equation} u_t=\frac12\sum_{i,j=1}^na_{ij}(x)u_{x_ix_j}+\sum_{i=1}^na_i(x)u_{x_i}\equiv Lu,\quad u(0,x)=\varphi(x),\quad x\in\mathbf R^n,\ t\in[0,T], \end{equation}
when the matrix $\bigl\{a_{ij}(x)\bigr\}$ is degenerate. A generalized solution is introduced with the help of an infinitesimal operator of a Markov process connected with the operator in (1). In the proof of the theorems we use probabilistic characteristics of this process.
Bibliography: 11 titles.
Received: 26.12.1969
Bibliographic databases:
UDC: 517.946+519.21
MSC: Primary 35D05, 35K15, 60H99, 60J90; Secondary 35B05, 35K05
Language: English
Original paper language: Russian
Citation: I. M. Sonin, “On uniqueness classes for degenerating parabolic equations”, Math. USSR-Sb., 14:4 (1971), 453–469
Citation in format AMSBIB
\Bibitem{Son71}
\by I.~M.~Sonin
\paper On uniqueness classes for degenerating parabolic equations
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 4
\pages 453--469
\mathnet{http://mi.mathnet.ru//eng/sm3266}
\crossref{https://doi.org/10.1070/SM1971v014n04ABEH002815}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=287167}
\zmath{https://zbmath.org/?q=an:0243.35050}
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  • https://doi.org/10.1070/SM1971v014n04ABEH002815
  • https://www.mathnet.ru/eng/sm/v127/i4/p459
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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