On exact solutions of the nonlinear heat equation

1Barannyk, AF
2Barannyk, TA
3Yuryk, II
1Institute of Mathematics, Pomeranian University, Slupsk, Poland
2V.G. Korolenko Poltava National Pedagogical University
3National University of Food Technologies, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 5:11-17
https://doi.org/10.15407/dopovidi2019.05.011
Section: Mathematics
Language: English
Abstract: 

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).

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

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