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

• Datum: 2026
• Hauptverfasser: Barannyk, T. A., Barannyk, A. F., Yuryk, I. I., Баранник, Т. А., Баранник, А. Ф., Юрик, І. І.
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2026
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/1527
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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 equati...