We propose a method for the construction of exact solutions to nonlinear heat equation based on the classical method of separation of variables, its generalization, and the Lie reduction method. We consider substitutions reducing the nonlinear heat equation to ordinary differential equations and construct the classes of exact solutions by the method of generalized separation of variables.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 3, pp. 294–310, March, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i3.6667.
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Barannyk, A.F., Barannyk, T.A. & Yuryk, I.I. Exact Solutions with Generalized Separation of Variables in the Nonlinear Heat Equation. Ukr Math J 74, 330–349 (2022). https://doi.org/10.1007/s11253-022-02066-6
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DOI: https://doi.org/10.1007/s11253-022-02066-6