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

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Abstract

The article is devoted to the construction and investigation of exact solutions with free boundary to a second-order nonlinear parabolic equation. The solutions belong to the classes of generalized self-similar and generalized traveling waves. Their construction is reduced to Cauchy problems for second-order ordinary differential equations (ODE), for which we prove existence and uniqueness theorems for their solutions. A qualitative analysis of the ODE is carried out by passing to a dynamical system and constructing and studying its phase portrait. In addition, we present geometric illustrations.

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  1. Matrosov Institute for System Dynamics and Control Theory, Irkutsk, 664033, Russia

    A. L. Kazakov

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Kazakov, A.L. Construction and Investigation of Exact Solutions with Free Boundary to a Nonlinear Heat Equation with Source. Sib. Adv. Math. 30, 91–105 (2020). https://doi.org/10.3103/S1055134420020029

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  • DOI: https://doi.org/10.3103/S1055134420020029

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