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Mat. Sb. (N.S.), 1973, Volume 91(133), Number 4(8), Pages 500–522 (Mi msb3313)  

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

Asymptotics of the fundamental solution of a Petrovskii parabolic equation with constant coefficients

S. G. Gindikin, M. V. Fedoryuk


Abstract: Let $P(\zeta)$, $\zeta\in\mathbf C^n$, be a homogeneous, parabolic polynomial of degree $2m$. Properties of the function
$$ \nu(\eta)=\min_{\xi\in\mathbf R^n}\operatorname{Re}P(\xi+i\eta),\qquad\eta\in\mathbf R^n, $$
are investigated. Two-sided estimates are obtained for the fundamental solution $G(t,x)$ of the equation
$$ \frac{\partial u}{\partial t}+P(\frac1i\frac\partial{\partial x})u=0, $$
and an asymptotic decomposition is determined for $G(t,x)$ as $|x|^{2m}/t\to+\infty$ under the assumption that $\nu(\eta)\in C^1(\mathbf R^n)$.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 20:4, 519–542

Bibliographic databases:

UDC: 517.947
MSC: 35K30, 35B40, 35E05
Received: 09.11.1972

Citation: S. G. Gindikin, M. V. Fedoryuk, “Asymptotics of the fundamental solution of a Petrovskii parabolic equation with constant coefficients”, Mat. Sb. (N.S.), 91(133):4(8) (1973), 500–522; Math. USSR-Sb., 20:4 (1973), 519–542

Citation in format AMSBIB
\Bibitem{GinFed73}
\by S.~G.~Gindikin, M.~V.~Fedoryuk
\paper Asymptotics of the fundamental solution of a~Petrovskii parabolic equation with constant coefficients
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 91(133)
\issue 4(8)
\pages 500--522
\mathnet{http://mi.mathnet.ru/msb3313}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=393850}
\zmath{https://zbmath.org/?q=an:0292.35043}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 20
\issue 4
\pages 519--542
\crossref{https://doi.org/10.1070/SM1973v020n04ABEH001889}


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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. G. Gindikin, M. V. Fedoryuk, “Saddle points of parabolic polynomials”, Math. USSR-Sb., 23:3 (1974), 362–381  mathnet  crossref  mathscinet  zmath
    2. M. M. Postnikov, “On the Asymptotics of the Green Functions for Parabolic Equations”, Proc. Steklov Inst. Math., 236 (2002), 260–272  mathnet  mathscinet  zmath
    3. S. A. Stepin, “Kernel estimates and the regularized trace of the semigroup generated by a potential perturbation of the bi-Laplacian”, Russian Math. Surveys, 66:3 (2011), 635–636  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. S. A. Stepin, “Asymptotic estimates for the kernel of the semigroup generated by a perturbation of the biharmonic operator by a potential”, Sb. Math., 203:6 (2012), 893–921  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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