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Construction and Investigation of Exact Solutions with Free Boundary to a Nonlinear Heat Equation with Source

Авторы: Kazakov A.L.

Журнал: Siberian Advances in Mathematics

Том: 30

Номер: 2

Год: 2020

Отчётный год: 2020

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Аннотация: The article is devoted to the construction and investigation of exact solutions with freeboundary to a second-order nonlinear parabolic equation. The solutions belong to the classes ofgeneralized self-similar and generalized traveling waves. Their construction is reduced to Cauchyproblems for second-order ordinary differential equations (ODE), for which we prove existence anduniqueness theorems for their solutions. A qualitative analysis of the ODE is carried out bypassing to a dynamical system and constructing and studying its phase portrait. In addition, wepresent geometric illustrations.

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