Abstract:
For the heat equation on a plane an asymptotic approximation of the solution of the Cauchy problem for large times is constructed in the case when the initial function at infinity has a power-like asymptotics. Investigation of the asymptotic behavior of the solution of the problem under consideration in addition to direct application to processes of heat conduction and diffusion has an independent interest for asymptotic analysis.
Citation:
S. V. Zakharov, “Asymptotic calculation of the heat distribution on a plane”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 93–99; Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 243–249
\Bibitem{Zak16}
\by S.~V.~Zakharov
\paper Asymptotic calculation of the heat distribution on a plane
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 1
\pages 93--99
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2017
\vol 296
\issue , suppl. 1
\pages 243--249
\crossref{https://doi.org/10.1134/S0081543817020237}
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Linking options:
https://www.mathnet.ru/eng/timm1263
https://www.mathnet.ru/eng/timm/v22/i1/p93
This publication is cited in the following 2 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
S. V. Zakharov, “Asymptotic solution of the multidimensional Burgers equation near a singularity”, Theoret. and Math. Phys., 196:1 (2018), 976–982
Citation in format AMSBIB
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