On exact solutions of the nonlinear heat equation

TitleOn exact solutions of the nonlinear heat equation
Publication TypeJournal Article
Year of Publication2019
AuthorsBarannyk, AF, Barannyk, TA, Yuryk, II
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published05/2019

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).

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

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