Sergey V. Zakharov     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya str., Ekaterinburg, 620108, Russian Federation)


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.


Multidimensional heat equation, Cauchy problem, Asymptotics, Auxiliary parameter method

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