Nonclassical solutions are non-existent for the heat equation and rare for nonlinear diffusion

DOI10.1006/jmaa.1996.0316zbMath0864.35019OpenAlexW2044522065MaRDI QIDQ1922995

Daniel J. Arrigo, Joanna M. Goard, Philip Broadbridge

Publication date: 13 November 1996

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

Full work available at URL: https://doi.org/10.1006/jmaa.1996.0316

zbMATH Keywords

invariant surface conditionnonclassical symmetries methodinfinitesimal Lie transformation

Mathematics Subject Classification ID

Heat equation (35K05) Invariance and symmetry properties for PDEs on manifolds (58J70) Solutions to PDEs in closed form (35C05)

Related Items (8)

On the determining equations for the nonclassical reductions of the heat and Burgers' equation ⋮ Symmetry analysis of the two-dimensional diffusion equation with a source term ⋮ Lie symmetry properties of nonlinear reaction-diffusion equations with gradient-dependent diffusivity ⋮ Symmetry approaches for reductions of PDEs, differential constraints and Lagrange-Charpit method ⋮ Group properties of generalized quasi-linear wave equations ⋮ An application of solvable structures to classical and nonclassical similarity solutions ⋮ The nonclassical group analysis of the heat equation ⋮ All solutions of standard symmetric linear partial differential equations have classical Lie symmetry

This page was built for publication: Nonclassical solutions are non-existent for the heat equation and rare for nonlinear diffusion