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Analytical diffusion wave-type solutions to a nonlinear parabolic system with cylindrical and spherical symmetry

Авторы: Kazakov A., Kuznetsov P.

Журнал: The Bulletin of Irkutsk State University. Series: Mathematics

Том: 37

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Год: 2021

Отчётный год: 2021

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Аннотация: The paper deals with a second-order nonlinear parabolic system that describes heat and mass transfer in a binary liquid mixture. The nature of nonlinearity is such that the system has a trivial solution where its parabolic type degenerates. This circumstance allows us to consider a class of solutions having the form of diffusion waves propagating over a zero background with a finite velocity. We focus on two spatially symmetric cases when one of the two independent variables is time, and the second is the distance to a certain point or line. The existence and uniqueness theorem of the diffusion wave-type solution with analytical components is proved. The solution is constructed as a power series with recursively determined coefficients, which convergence is proved by the majorant method. In one particular case, we reduce the considered problem to the Cauchy problem for a system of ordinary differential equations that inherits all the specific features of the original one...

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