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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 4(8), Pages 459–473 (Mi msb3266)  

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

On uniqueness classes for degenerating parabolic equations

I. M. Sonin


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 $\{a_{ij}(x)\}$ 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.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:4, 453–469

Bibliographic databases:

UDC: 517.946+519.21
MSC: Primary 35D05, 35K15, 60H99, 60J90; Secondary 35B05, 35K05
Received: 26.12.1969

Citation: I. M. Sonin, “On uniqueness classes for degenerating parabolic equations”, Mat. Sb. (N.S.), 85(127):4(8) (1971), 459–473; 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 Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 4(8)
\pages 459--473
\mathnet{http://mi.mathnet.ru/msb3266}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=287167}
\zmath{https://zbmath.org/?q=an:0243.35050}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 4
\pages 453--469
\crossref{https://doi.org/10.1070/SM1971v014n04ABEH002815}


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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. O. A. Oleinik, E. V. Radkevich, “The method of introducing a parameter in the study of evolutionary equations”, Russian Math. Surveys, 33:5 (1978), 7–84  mathnet  crossref  mathscinet  zmath
    2. Akhmetov D.R. Lavrentiev Jr. Mikhail M. Spigler R., “Singular Perturbations for Parabolic Equations with Unbounded Coefficients Leading to Ultraparabolic Equations”, Differ. Integral Equ., 17:1-2 (2004), 99–118  mathscinet  zmath  isi
    3. V. F. Vil'danova, F. Kh. Mukminov, “Anisotropic uniqueness classes for a degenerate parabolic equation”, Sb. Math., 204:11 (2013), 1584–1597  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. V. F. Vil'danova, F. Kh. Mukminov, “Täcklind uniqueness classes for heat equation on noncompact Riemannian manifolds”, Ufa Math. J., 7:2 (2015), 55–63  mathnet  crossref  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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