Exact solutions of nonlinear heat equation $u_t=(F(u)u_x)_x+H(u)$

• Date: 2019
• Main Authors: Barannyk, A., Barannyk, T., Yuryk, I., Баранник, А., Баранник, Т., Юрик, І.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2019
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/363
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

A method for construction of exact solutions to nonlinear heat equation $u_t=(F(u)u_x)_x+H(u)$ which is based on ansatz $p(x)=w_1(t)\varphi(u)$ is proposed. Here the function $p(x)$ is a solution to one of the equations $(p')^2 = Ap^2 + B$, $(p')^2 = Ap^4 + Bp^2 +C$, and the functi...