A method for the construction of exact solutions to the nonlinear heat equation \(u_t = (F(U)U_x)_X + G(U)U_{x} + H(U)\)

DOI10.1007/S11253-020-01739-4zbMath1503.35054OpenAlexW3027091984MaRDI QIDQ2100681

Ivan I. Yuryk, Tatjana A. Barannyk, Anatoliy F. Barannyk

Publication date: 24 November 2022

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-020-01739-4

zbMATH Keywords

separation of variables

Mathematics Subject Classification ID

Solutions to PDEs in closed form (35C05) Quasilinear parabolic equations (35K59)

Related Items (1)

Exact solutions with generalized separation of variables in the nonlinear heat equation

Cites Work

• Generalized separation of variables for nonlinear equation \(u_{tt} = F(u)u_{xx} + aF'(u)u_x^2\)
• Separation of variables for nonlinear equations of hyperbolic and Korteweg-de Vries type
• Solitary wave and other solutions for nonlinear heat equations
• On invariant solutions of the equation of non-linear heat conduction with a source
• Positivity versus localization in degenerate diffusion equations
• О Некоторых свойствах обобщенных решений квазилинейных вырождающихся параболических уравнений
• Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
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