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Mat. Zametki, 1968, Volume 3, Issue 2, Pages 171–178 (Mi mz6664)  

This article is cited in 1 scientific paper (total in 2 paper)

Increasing solutions of linear second-order equations with nonnegative characteristic form

A. S. Kalashnikov

M. V. Lomonosov Moscow State University

Abstract: In a layer $H\{0<t\le T, x\in R^n\}$ we consider a linear second-order parabolic equation that degenerates on an arbitrary subset $\overline H$. It is assumed that the coefficient of the time derivative has a zero of sufficiently high order on the hyperplane $t=0$; as a consequence, the Cauchy problem will be unsolvable. The exact bounds are obtained of the permissible growth of the sought-for function when $|x|\to\infty$, ensuring a single-valued solution of the problem without initial data.

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English version:
Mathematical Notes, 1968, 3:2, 110–114

Bibliographic databases:

UDC: 517.9
Received: 06.09.1967

Citation: A. S. Kalashnikov, “Increasing solutions of linear second-order equations with nonnegative characteristic form”, Mat. Zametki, 3:2 (1968), 171–178; Math. Notes, 3:2 (1968), 110–114

Citation in format AMSBIB
\Bibitem{Kal68}
\by A.~S.~Kalashnikov
\paper Increasing solutions of linear second-order equations with nonnegative characteristic form
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 2
\pages 171--178
\mathnet{http://mi.mathnet.ru/mz6664}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=249831}
\zmath{https://zbmath.org/?q=an:0179.42804}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 2
\pages 110--114
\crossref{https://doi.org/10.1007/BF01094330}


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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. A. S. Kalashnikov, “O neogranichennykh resheniyakh nekotorykh lineinykh vyrozhdayuschikhsya parabolicheskikh sistem vtorogo poryadka”, UMN, 25:2(152) (1970), 271–272  mathnet  mathscinet  zmath
    2. T. D. Venttsel', Yu. A. Dubinskii, A. M. Il'in, V. A. Kondrat'ev, V. P. Mikhailov, A. A. Mal'tsev, O. A. Oleinik, S. I. Pokhozhaev, N. Kh. Rozov, G. A. Chechkin, T. A. Shaposhnikova, “Anatolii Sergeevich Kalashnikov (obituary)”, Russian Math. Surveys, 55:5 (2000), 977–985  mathnet  crossref  crossref  mathscinet  adsnasa  isi
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