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Analytical and numerical solutions to the problem on a heat wave initiating for the nonlinear heat equation with a source

Авторы: Kazakov A.L., Kuznetsov P.A., Lempert A.A., Spevak L.F.

Журнал: Journal of Physics: Conference series

Том: 1268

Номер:

Год: 2019

Отчётный год: 2019

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Аннотация: The article deals with the nonlinear heat (porous medium) equation with a source. This equation has a large number of applications, as well as non-standard non-linear properties. An important class of solutions to the equation is heat waves (waves of filtration), propagating on a zero background with a finite velocity. This paper continues the cycle of articles devoted to the construction and study of heat waves with a closed front. Here we consider a problem with a given boundary condition with a source in cases of plane, circular and spherical symmetry. The solution is constructed in the form of a double power series, the theorem of existence and uniqueness is proved. We also look for some exact solutions of an equation with a power source, the construction of which reduces to the integration of ordinary differential equations (ODE) with a singularity. To solve the obtained ODE, we propose a computational algorithm based on the boundary element method. The results of numerical calculations are presented and discussed.

Индексируется WOS: 1

Индексируется Scopus: 0

Индексируется РИНЦ: 0

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