The nonclassical group analysis of the heat equation

DOI10.1006/jmaa.1998.6250zbMath0928.35007OpenAlexW1978375672MaRDI QIDQ1283115

Elizabeth L. Mansfield

Publication date: 19 January 2000

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1998.6250

zbMATH Keywords

Burger's equationsecondary differential equations

Mathematics Subject Classification ID

Invariance and symmetry properties for PDEs on manifolds (58J70) Other special methods applied to PDEs (35A25)

Related Items (11)

On the determining equations for the nonclassical reductions of the heat and Burgers' equation ⋮ Transformation properties of a variable-coefficient Burgers equation ⋮ Reduction operators and exact solutions of generalized Burgers equations ⋮ Nonclassical symmetry solutions for fourth-order phase field reaction-diffusion ⋮ Extended symmetry analysis of generalized Burgers equations ⋮ Nonclassical symmetries of evolutionary partial differential equations and compatibility. ⋮ On the derivation of nonclassical symmetries of the Black-Scholes equation via an equivalence transformation ⋮ Classical and nonclassical Lie symmetry analysis to a class of nonlinear time-fractional differential equations ⋮ Reduction operators of Burgers equation ⋮ Singular reduction modules of differential equations ⋮ Classical integrability for beta-ensembles and general Fokker-Planck equations

Uses Software

• diffgrob2

Cites Work

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• Painlevé analysis of a coupled Burgers-heat equation system, and non- classical similarity solutions of the heat equation
• On the weak symmetry groups of partial differential equations
• Similarity methods for differential equations
• Nonclassical symmetries and Bäcklund transformations
• Symmetry reductions and exact solutions of a class of nonlinear heat equations
• Iterating the nonclassical symmetries method
• Nonclassical symmetry reductions of the Boussinesq equation
• Nonclassical solutions are non-existent for the heat equation and rare for nonlinear diffusion
• The construction of special solutions to partial differential equations
• On a shallow water wave equation
• Direct reduction and differential constraints
• Algorithms for the Nonclassical Method of Symmetry Reductions
• Nonlinear interaction of traveling waves of nonintegrable equations
• Geometric Approach to Invariance Groups and Solution of Partial Differential Systems
• Symmetry-based algorithms to relate partial differential equations: I. Local symmetries

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