|1Barannyk, AF |
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|
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|
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