2019
Том 71
№ 11

# A method for the construction of exact solutions to the nonlinear heat equation $u_t = \left(F(u)u_x \right)_x +G(u)u_x +H(u)$

Abstract

UDC 517.9
We propose a method for the construction of exact solutions to the nonlinear heat equation based on the classical method of separation of variables and its generalization. We consider substitutions used to reduce the nonlinear heat equation to a system of two ordinary differential equations and construct the classes of exact solutions by the method of generalized separation of variables.

Citation Example: Barannyk A. F., Barannyk T. A., Yuryk I. I. A method for the construction of exact solutions to the nonlinear heat equation $u_t = \left(F(u)u_x \right)_x +G(u)u_x +H(u)$ // Ukr. Mat. Zh. - 2019. - 71, № 11. - pp. 1443 -1454.