Geodesic
Construction and investigation of exact solutions with free boundary to a~nonlinear heat equation with source
Matematičeskie trudy, Tome 22 (2019) no. 2, pp. 54-75.

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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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A. L. Kazakov. Construction and investigation of exact solutions with free boundary to a~nonlinear heat equation with source. Matematičeskie trudy, Tome 22 (2019) no. 2, pp. 54-75. http://geodesic.mathdoc.fr/item/MT_2019_22_2_a3/

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