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Mat. Sb. (N.S.), 1987, Volume 132(174), Number 3, Pages 322–344 (Mi msb1857)  

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

Asymptotics of a fundamental solution of a parabolic equation as $t\to\infty$

E. F. Lelikova


Abstract: The author analyzes the behavior as $t\to\infty$ of the fundamental solution $G(x, s, t)$ of the Cauchy problem for the equation $v_t-v_{xx}-a(x)v_x-b(x)v=0$ with infinitely differentiable coefficients $a(x)$ and $b(x)$ decreasing as $|x|\to\infty$. For the case when the functions $a(x)$ and $b(x)$ can be expanded as $x\to\pm\infty$ on asymptotic series of the form
\begin{gather*} a(x)=a_1|x|^{-\alpha_1}+…+a_i|x|^{-\alpha_i}+…,
b(x)=b_1|x|^{-\beta_1}+…+b_i|x|^{-\beta_i}+…, \end{gather*}
where $\alpha_m$, $\beta_m\uparrow\infty$ as $m\to\infty$, $\alpha_1>1$, $\beta_1>2$, she constructs and justifies asymptotic expansion of the fundamental solution $G(x, s, t)$ to within any power of $G(x, s, t)$ uniformly with respect to all $x$ and $s$ in $\mathbf R^1$.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Sbornik, 1988, 60:2, 315–337

Bibliographic databases:

UDC: 517.95
MSC: Primary 35K15, 35B40; Secondary 41A60
Received: 09.12.1985

Citation: E. F. Lelikova, “Asymptotics of a fundamental solution of a parabolic equation as $t\to\infty$”, Mat. Sb. (N.S.), 132(174):3 (1987), 322–344; Math. USSR-Sb., 60:2 (1988), 315–337

Citation in format AMSBIB
\Bibitem{Lel87}
\by E.~F.~Lelikova
\paper Asymptotics of~a~fundamental solution of~a~parabolic equation as~ $t\to\infty$
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 132(174)
\issue 3
\pages 322--344
\mathnet{http://mi.mathnet.ru/msb1857}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=889595}
\zmath{https://zbmath.org/?q=an:0706.35014}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 60
\issue 2
\pages 315--337
\crossref{https://doi.org/10.1070/SM1988v060n02ABEH003171}


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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. E. F. Lelikova, “On the asymptotics of the fundamental solution of a parabolic equation in the critical case”, Math. USSR-Sb., 67:2 (1990), 581–594  mathnet  crossref  mathscinet  zmath  isi
    2. Lelikova E., “On the Asymptotics of the Fundamental Solution of Parabolic Equation in Critical Case”, 312, no. 3, 1990, 532–535  mathscinet  zmath  isi
    3. E. F. Lelikova, “Asymptotic behaviour of the fundamental solution of a second-order parabolic equation”, Sb. Math., 186:4 (1995), 591–609  mathnet  crossref  mathscinet  zmath  isi
    4. Lelikova E., “On the Asymptotics of the Fundamental Solution of Some High-Order Parabolic Equation”, Dokl. Akad. Nauk, 341:5 (1995), 590–593  mathnet  mathscinet  zmath  isi
    5. D. O. Degtyarev, A. M. Il'in, “The asymptotics of a solution of a parabolic equation as time increases without bound”, Sb. Math., 203:11 (2012), 1589–1610  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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