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A Method for the Construction of Exact Solutions to the Nonlinear Heat Equation Ut = (F(U)Ux)X + G(U)Ux + H(U)

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Ukrainian Mathematical Journal Aims and scope

We propose a method for the construction of exact solutions to the nonlinear heat equation based on the classical method of separation of variables and its generalization. We consider substitutions, which reduce the nonlinear heat equation to a system of two ordinary differential equations and construct the classes of exact solutions by the method of generalized separation of variables.

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Authors and Affiliations

  1. Pomeranian Academy, Słupsk, Poland

    A. F. Barannyk

  2. Poltava National Pedagogical University, Poltava, Ukraine

    T. A. Barannyk

  3. National University of Food Technologies, Kyiv, Ukraine

    I. I. Yuryk

Authors
  1. A. F. Barannyk
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  2. T. A. Barannyk
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  3. I. I. Yuryk
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Corresponding authors

Correspondence to T. A. Barannyk or I. I. Yuryk.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 11, pp. 1443–1454, November, 2019.

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Barannyk, A.F., Barannyk, T.A. & Yuryk, I.I. A Method for the Construction of Exact Solutions to the Nonlinear Heat Equation Ut = (F(U)Ux)X + G(U)Ux + H(U). Ukr Math J 71, 1651–1663 (2020). https://doi.org/10.1007/s11253-020-01739-4

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  • DOI: https://doi.org/10.1007/s11253-020-01739-4

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