On exact solutions of the nonlinear heat equation


  • A.F. Barannyk Institute of Mathematics, Pomeranian University, Słupsk, Poland
  • T.A. Barannyk Poltava V.G. Korolenko National Pedagogical University
  • I.I. Yuryk National University of Food Technologies, Kiev




exact solutions, generalized variable separation, group-theoretic methods, nonlinear heat equation


A method for construction of exact solutions to the nonlinear heat equation ut = (F (u)ux)x + G (u)ux + H (u), which is based on the ansatz p(x) = ω1(t) φ(u) + ω2(t), is proposed. The function p(x) is a solution of the equation (p′)2 = Ap2 + B, and the functions ω1(t), ω2(t) and ϕ(u) can be found from the condition that this ansatz reduces the nonlinear heat equation to a system of two ordinary differential equations with unknown functions ω1(t) and ω2(t).


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How to Cite

Barannyk, A., Barannyk, T., & Yuryk, I. (2024). On exact solutions of the nonlinear heat equation . Reports of the National Academy of Sciences of Ukraine, (5), 11–17. https://doi.org/10.15407/dopovidi2019.05.011