TY - JOUR AU - T. A. Barannyk AU - A. F. Barannyk AU - I. I. Yuryk PY - 2019/11/25 Y2 - 2024/03/29 TI - A method for the construction of exact solutions to the nonlinear heat equation $u_t = \left(F(u)u_x \right)_x +G(u)u_x +H(u)$ JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 71 IS - 11 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1527 AB - 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. ER -