Exact solutions of the generalized Richards equation with power-law nonlinearities

DOI10.1134/S0012266120090025zbMath1450.35101OpenAlexW3092271641MaRDI QIDQ2004004

Alexander Arkad'evich Kosov, Edward Ivanovich Semenov

Publication date: 14 October 2020

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266120090025

zbMATH Keywords

filtration in porous mediaLambert's \(W \)-function

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Solutions to PDEs in closed form (35C05) Semilinear parabolic equations (35K58)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exact solutions of diffusion-convection equations
• Group classification and symmetry reductions of the nonlinear diffusion- convection equation \(u_ t=(D(u)u_ x)_ x-K'(u)u_ x\)
• New exact solutions to the one-dimensional nonlinear diffusion equation
• Intermediate asymptotics for Richards' equation in a finite layer
• On new exact solutions of the one-dimensional nonlinear diffusion equation with a source (sink)
• An approximate analytical solution of Richards equation with finite boundary
• On the Lambert \(w\) function
• Construction of exact solutions of one-dimensional nonlinear diffusion by the method of linear invariant subspaces
• The Lambert function and exact solutions of nonlinear parabolic equations
• Attractors in models of porous media flow
• New results on group classification of nonlinear diffusion–convection equations
• Nonclassical symmetry reductions of a porous medium equation with convection