Symmetries and form-preserving transformations of generalised inhomogeneous nonlinear diffusion equations

DOI10.1016/S0378-4371(03)00063-3zbMath1024.35042MaRDI QIDQ1566161

Christodoulos Sophocleous

Publication date: 1 June 2003

Published in: Physica A (Search for Journal in Brave)

zbMATH Keywords

nonlocal transformationsnew exact solutionsLie-Bäcklund symmetries

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Invariance and symmetry properties for PDEs on manifolds (58J70) Solutions to PDEs in closed form (35C05) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (15)

Conditional Lie-Bäcklund symmetries to inhomogeneous nonlinear diffusion equations ⋮ On the equivalence groups for (2+1) dimensional nonlinear diffusion equation ⋮ On the classification of similarity solutions of a two-dimensional diffusion-advection equation ⋮ Radial equivalence of nonhomogeneous nonlinear diffusion equations ⋮ Generation solutions algorithms for the class of inhomogeneous nonlinear diffusion equations ⋮ Symmetry analysis and group-invariant solutions to inhomogeneous nonlinear diffusion equation ⋮ On the group classification of variable-coefficient nonlinear diffusion--convection equations ⋮ Invariant subspaces and conditional Lie-Bäcklund symmetries of inhomogeneous nonlinear diffusion equations ⋮ Group classification of systems of diffusion equations ⋮ Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities ⋮ Conditional Lie-Bäcklund symmetries and reductions of the nonlinear diffusion equations with source ⋮ Nonlocal symmetries of systems of evolution equations ⋮ Lie group analysis of a flow with contaminant-modified viscosity ⋮ Classical Lie point symmetry analysis of nonlinear diffusion equations describing thermal energy storage ⋮ Symmetry reductions and solutions for pollutant diffusion in a cylindrical system

Cites Work

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• Similarity solutions for nonlinear diffusion - A new integration procedure
• Similarity solutions for nonlinear diffusion - Further exact solutions
• Nonlocal symmetries. Heuristic approach
• Symmetry and integration methods for differential equations
• Classification of potential symmetries of generalised inhomogeneous nonlinear diffusion equations
• Exact similarity solutions to some nonlinear diffusion equations
• Exact solutions to a nonlinear diffusion equation
• New classes of symmetries for partial differential equations
• On form-preserving point transformations of partial differential equations
• On the remarkable nonlinear diffusion equation (∂/∂x)[a (u+b)−2(∂u/∂x)−(∂u/∂t)=0]
• Propagation of thermal waves in an inhomogeneous medium
• Group Transformations and the Nonlinear Heat Diffusion Equation
• Non-linear diffusion in a finite mass medium
• Nonlinear thermal evolution in an inhomogeneous medium
• On symmetries of radially symmetric nonlinear diffusion equations
• Evolution equations possessing infinitely many symmetries
• On point transformations of generalized nonlinear diffusion equations
• Classification of the Extended Symmetries of the Inhomogeneous Nonlinear Diffusion Equation
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• Symmetry-based algorithms to relate partial differential equations: I. Local symmetries

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