New selfsimilar solutions of the porous medium equation and the theory of solutions of changing sign

DOI10.1016/0362-546X(90)90076-SzbMath0734.35042MaRDI QIDQ3361224

Juan Luis Vazquez

Publication date: 1990

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

growth ratesporous medium equationoscillatory

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Flows in porous media; filtration; seepage (76S05) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items

Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type ⋮ Fundamental solution and long time behavior of the porous medium equation in hyperbolic space ⋮ Radial equivalence for the two basic nonlinear degenerate diffusion equations ⋮ Similarity solutions of the porous medium equation with sign changes ⋮ Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large time behaviour of solutions of the porous medium equation in bounded domains
• On a class of similarity solutions of the porous media equation
• On a class of similarity solutions of the porous media equation. II
• Regularity of solutions and interfaces of the porous medium equation via local estimates
• The Interfaces of One-Dimensional Flows in Porous Media
• The Initial Trace of a Solution of the Porous Medium Equation
• Asymptotic Behaviour and Propagation Properties of the One-Dimensional Flow of Gas in a Porous Medium
• The interface between regions where u<0 andu > 0in the porous medium equation