Similarity solutions of the porous medium equation with sign changes
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Publication:5905402
DOI10.1016/0022-247X(91)90138-PzbMath0777.35034OpenAlexW2044954077MaRDI QIDQ5905402
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
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 ut(|u|m−1ux)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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