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Mat. Zametki, 1969, Volume 6, Issue 1, Pages 97–108 (Mi mz6902)  

This article is cited in 4 scientific papers (total in 5 papers)

Results concerning the nature of the continuity of solutions of parabolic equations and some of their applications

S. N. Kruzhkov

M. V. Lomonosov Moscow State University

Abstract: Theorems are established which deal with the relationship between the moduli of continuity with respect to $x$ and with respect to $t$ (in the spaces $C$ and $L_1$) for the solutions of certain classes of parabolic equations, which are, in general, nonlinear and degenerate. These theorems are then applied to an investigation of the Cauchy problem for quasilinear equations of the first and second order.

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English version:
Mathematical Notes, 1969, 6:1, 571–523

Bibliographic databases:

UDC: 517.9
Received: 30.12.1968

Citation: S. N. Kruzhkov, “Results concerning the nature of the continuity of solutions of parabolic equations and some of their applications”, Mat. Zametki, 6:1 (1969), 97–108; Math. Notes, 6:1 (1969), 571–523

Citation in format AMSBIB
\Bibitem{Kru69}
\by S.~N.~Kruzhkov
\paper Results concerning the nature of the continuity of solutions of parabolic equations and some of their applications
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 1
\pages 97--108
\mathnet{http://mi.mathnet.ru/mz6902}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=249832}
\zmath{https://zbmath.org/?q=an:0177.14205}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 1
\pages 571--523
\crossref{https://doi.org/10.1007/BF01450257}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. N. Kruzhkov, “First order quasilinear equations in several independent variables”, Math. USSR-Sb., 10:2 (1970), 217–243  mathnet  crossref  mathscinet  zmath
    2. A. V. Faminskii, “The Cauchy problem for the Korteweg–de Vries equation when the initial data are irregular”, Russian Math. Surveys, 36:3 (1981), 248–249  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. S. N. Kruzhkov, A. V. Faminskii, “Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation”, Math. USSR-Sb., 48:2 (1984), 391–421  mathnet  crossref  mathscinet  zmath
    4. A. S. Kalashnikov, “Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations”, Russian Math. Surveys, 42:2 (1987), 169–222  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. N. S. Bakhvalov, M. I. Zelikin, A. S. Kalashnikov, V. L. Kamynin, O. A. Oleinik, E. Yu. Panov, N. S. Petrosyan, V. M. Tikhomirov, A. V. Faminskii, V. N. Chubarikov, “Stanislav Nikolaevich Kruzhkov (obituary)”, Russian Math. Surveys, 53:5 (1998), 1071–1078  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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