Similarity solutions of the porous medium equation with sign changes

DOI10.1016/0022-247X(91)90138-PzbMath0777.35034OpenAlexW2044954077MaRDI QIDQ5905402

Josephus Hulshof

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1016/0022-247x(91)90138-p

zbMATH Keywords

nonlinear diffusionBarenblatt-Pattle solutionsdipole solutionssemilarity solutions

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Reaction-diffusion equations (35K57) Flows in porous media; filtration; seepage (76S05) Degenerate parabolic equations (35K65)

Related Items (16)

Unnamed Item ⋮ Anomalous large-time behaviour of the \(p\)-Laplacian flow in an exterior domain in low dimension ⋮ A selfsimilar solution to the focusing problem for the porous medium equation ⋮ Radial equivalence of nonhomogeneous nonlinear diffusion equations ⋮ Cauchy-Dirichlet problems for the porous medium equation ⋮ The blow-up profile for a fast diffusion equation with a nonlinear boundary condition ⋮ Asymptotic behaviour of ground states ⋮ On nonexistence of Baras-Goldstein type without positivity assumptions for singular linear and nonlinear parabolic equations ⋮ Radial equivalence for the two basic nonlinear degenerate diffusion equations ⋮ Similarity solutions of the porous medium equation with sign changes ⋮ Unnamed Item ⋮ An asymptotic approach to second-kind similarity solutions of the modified porous-medium equation ⋮ Maximal viscosity solutions of the modified porous medium equation and their asymptotic behaviour ⋮ Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations ⋮ Solving a nonlinear variation of the heat equation: self-similar solutions of the second kind and other results ⋮ Self-similar solutions satisfying or not the equation of the interface.

Cites Work

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• On a class of similarity solutions of the porous media equation. III
• On a class of similarity solutions of the porous media equation
• On a class of similarity solutions of the porous media equation. II
• New selfsimilar solutions of the porous medium equation and the theory of solutions of changing sign
• On a Class of Similarity Solutions of the Equation u_t(|u|^m−1u_x)_x with m −1
• Analyticity of the Interface of the Porous Media Equation After the Waiting Time
• The interface between regions where u<0 andu > 0in the porous medium equation
• Asymptotic Behaviour of Solutions of the Porous Medium Equation with Changing Sign
• A class of similarity solutions of the nonlinear diffusion equation
• On reducible non-linear differential equations occurring in mechanics
• Similarity solutions of the porous medium equation with sign changes

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