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Title: | The Asymptotics of a Solution of the Multidimensional Heat Equation with Unbounded Initial Data |
Authors: | Zakharov, S. V. |
Issue Date: | 2021 |
Publisher: | N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences Ural Federal University named after the first President of Russia B.N. Yeltsin |
Citation: | Zakharov S. V. The Asymptotics of a Solution of the Multidimensional Heat Equation with Unbounded Initial Data / S. V. Zakharov. — DOI 10.15826/umj.2021.1.013. — Text : electronic // Ural Mathematical Journal. — 2021. — Volume 7. — № 1. — P. 168-177. |
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. |
Keywords: | MULTIDIMENSIONAL HEAT EQUATION CAUCHY PROBLEM ASYMPTOTICS AUXILIARY PARAMETER METHOD |
URI: | http://elar.urfu.ru/handle/10995/108575 |
Access: | Creative Commons Attribution License |
License text: | https://creativecommons.org/licenses/by/4.0/ |
ISSN: | 2414-3952 |
DOI: | 10.15826/umj.2021.1.013 |
Origin: | Ural Mathematical Journal. 2021. Volume 7. № 1 |
Appears in Collections: | Ural Mathematical Journal |
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