Integrable forms of the one-dimensional flow equation for unsaturated heterogeneous porous media

DOI10.1063/1.528001zbMath0651.76041OpenAlexW1986449838MaRDI QIDQ3796913

Philip Broadbridge

Publication date: 1988

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528001

zbMATH Keywords

Lie-Bäcklund symmetry groupnonlinear one-dimensional flowunsaturated heterogeneous porous medium

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Partial differential equations of mathematical physics and other areas of application (35Q99) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (12)

A nonlinear supercooled Stefan problem ⋮ Exact solvability of the Mullins nonlinear diffusion model of groove development ⋮ Steady unsaturated flow in two-dimensional scale-heterogeneous porous media ⋮ On transport through heterogeneous media: application of conjugated reciprocal transformations ⋮ Explicit solution for a Stefan problem with variable latent heat and constant heat flux boundary conditions ⋮ On the group classification of variable-coefficient nonlinear diffusion--convection equations ⋮ On a class of reciprocal Stefan moving boundary problems ⋮ Explicit solutions to the one-phase Stefan problem with temperature-dependent thermal conductivity and a convective term ⋮ Moving Boundary Problems for Heterogeneous Media. Integrability via Conjugation of Reciprocal and Integral Transformations ⋮ Integrable heterogeneous nonlinear Schrödinger equations with dielectric loss: Lie–Bäcklund symmetries ⋮ On Stefan-type moving boundary problems with heterogeneity: canonical reduction via conjugation of reciprocal transformations ⋮ Unnamed Item

Cites Work

• Exact solutions in nonlinear diffusion
• On two phase filtration under gravity and with boundary infiltration: application of a bäcklund transformation
• Immiscible two-phase flow in a porous medium: Utilization of a Laplace transform boost
• On the remarkable nonlinear diffusion equation (∂/∂x)[a (u+b)−2(∂u/∂x)−(∂u/∂t)=0]
• Group Transformations and the Nonlinear Heat Diffusion Equation
• 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]
• CAPILLARY CONDUCTION OF LIQUIDS THROUGH POROUS MEDIUMS
• Non-integrability of non-linear diffusion-convection equations in two-spatial dimensions
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics

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