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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 1(5), Pages 74–97 (Mi msb2373)  

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

Theorems of Wiman–Valiron type for solutions of parabolic equations

N. M. Suleimanov


Abstract: In this paper estimates of Wiman–Valiron type are established for solutions of evolution equations of the form
\begin{equation} u'(t)+A(t)u(t)=0 \end{equation}
in a Hilbert space, where $A(t)$ is a positive definite selfadjoint operator with discrete spectrum. In the case of a constant operator $A$ the results characterize the rate of growth of the function $\|u(t)\|$ as $t\to+0$ in terms of the rate of growth of the Fourier coefficients of the initial data.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 43:1, 63–84

Bibliographic databases:

UDC: 517.95
MSC: Primary 35K22, 35B40; Secondary 30D15
Received: 21.04.1980

Citation: N. M. Suleimanov, “Theorems of Wiman–Valiron type for solutions of parabolic equations”, Mat. Sb. (N.S.), 115(157):1(5) (1981), 74–97; Math. USSR-Sb., 43:1 (1982), 63–84

Citation in format AMSBIB
\Bibitem{Sul81}
\by N.~M.~Suleimanov
\paper Theorems of Wiman--Valiron type for solutions of parabolic equations
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 1(5)
\pages 74--97
\mathnet{http://mi.mathnet.ru/msb2373}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=618588}
\zmath{https://zbmath.org/?q=an:0494.35049|0467.35055}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 1
\pages 63--84
\crossref{https://doi.org/10.1070/SM1982v043n01ABEH002410}


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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. Suleimanov N., “One of the Refinements of Wiman-Valiron-Type Estimates for Solutions of Evolutional Equations”, 265, no. 3, 1982, 545–546  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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