Abstract:
For the multidimensional heat equation, the long-time asymptotic approximation of the solution of the Cauchy problem is obtained in the case when the initial function grows at infinity and contains logarithms in its asymptotics. In addition to natural applications to processes of heat conduction and diffusion, the investigation of the asymptotic behavior of the solution of the problem under consideration is of interest for the asymptotic analysis of equations of parabolic type. The auxiliary parameter method plays a decisive role in the investigation.
Citation:
Sergey V. Zakharov, “The asymptotics of a solution of the multidimensional heat equation with unbounded initial data”, Ural Math. J., 7:1 (2021), 168–177
\Bibitem{Zak21}
\by Sergey~V.~Zakharov
\paper The asymptotics of a solution of the multidimensional heat equation with unbounded initial data
\jour Ural Math. J.
\yr 2021
\vol 7
\issue 1
\pages 168--177
\mathnet{http://mi.mathnet.ru/umj145}
\crossref{https://doi.org/10.15826/umj.2021.1.013}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4301221}
\zmath{https://zbmath.org/?q=an:1475.35069}
\elib{https://elibrary.ru/item.asp?id=46381222}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85111989068}
Linking options:
https://www.mathnet.ru/eng/umj145
https://www.mathnet.ru/eng/umj/v7/i1/p168
This publication is cited in the following 1 articles:
S. V. Zakharov, “Constructing the asymptotics of a solution of the heat equation from the known asymptotics of the initial function in three-dimensional space”, Sb. Math., 215:1 (2024), 101–118
Citation in format AMSBIB
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