The integrable nonlinear degenerate diffusion equation \(u_ t=[f(u)u_ x^{-1}]_ x\) and its relatives

DOI10.1007/BF00920043zbMath0880.35095MaRDI QIDQ1366332

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

Publication date: 10 September 1997

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

explicit solutionsnonlinear diffusion equationsimilarity reductionssymmetry analysisturbulent transportstress dissipation in rock blasting

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) PDEs in connection with fluid mechanics (35Q35) Invariance and symmetry properties for PDEs on manifolds (58J70) Solutions to PDEs in closed form (35C05)

Related Items (4)

Hodograph-type transformations ⋮ Hodograph-Type Transformations for Linearization of Systems of Nonlinear Diffusion Equations ⋮ Symmetry classifications and reductions of some classes of \((2+1)\)-nonlinear heat equation ⋮ Hodograph Transformations and Cauchy Problem to Systems of Nonlinear Parabolic Equations

Cites Work

• Unnamed Item
• Hyperbolic phenomena in a strongly degenerate parabolic equation
• On the diffusion of biological populations
• Hodograph Transformations of Linearizable Partial Differential Equations
• A MATHEMATICAL MODEL FOR ROCK BLASTING INVOLVING A DEGENERATE NONLINEAR DIFFUSION EQUATION
• Inverse transformations and the reduction of nonlinear Dirichlet problems
• A symmetry approach to exactly solvable evolution equations
• On the exactly solvable equation$S_t = [ ( \beta S + \gamma )^{ - 2} S_x _x + \alpha ( \beta S + \gamma )^{ - 2} S_x $ Occurring in Two-Phase Flow in Porous Media]
• A Degenerate Pseudoparabolic Regularization of a Nonlinear Forward-Backward Heat Equation Arising in the Theory of Heat and Mass Exchange in Stably Stratified Turbulent Shear Flow
• On a nonlinear reaction-diffusion boundary-value problem: application of a Lie-Bäcklund symmetry
• Symmetries and differential equations

This page was built for publication: The integrable nonlinear degenerate diffusion equation \(u_ t=[f(u)u_ x^{-1}]_ x\) and its relatives