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A Heat Wave Problem for a Degenerate Nonlinear Parabolic Equation with a Specified Source Function

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

Журнал: AIP Conference Proceedings

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Год: 2018

Отчётный год: 2018

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Аннотация: A nonlinear parabolic heat conduction equation with a source is discussed, for which solutions of the heat wave propagating against a cold background at a finite velocity are studied. A new theorem of the existence and uniqueness of heat waves is proved. A particular case is studied in detail, when the heat wave is invariant and its construction reduces to solving an ordinary differential equation. For the numerical construction of invariant heat waves, an algorithm based on the boundary element method is proposed. Test examples are solved.

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