Boundary layer formation in the transition from the porous media equation to a Hele-Shaw flow.

DOI10.1016/S0294-1449(02)00016-1zbMath1030.35107MaRDI QIDQ1868104

Fernando Quirós, Omar Gil

Publication date: 27 April 2003

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2003__20_1_13_0

zbMATH Keywords

boundary layerfree boundarysingular limitporous media equationCauchy-Dirichlet problemsmesa problemconvergence of positivity sets

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Flows in porous media; filtration; seepage (76S05) Degenerate parabolic equations (35K65) Free boundary problems for PDEs (35R35) Other free boundary flows; Hele-Shaw flows (76D27)

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Cites Work

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• Obstructions to existence in fast-diffusion equations
• On the Mesa problem
• Some \(L^ 1\) existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions
• A singular limit problem for the porous medium equation
• The mesa-limit of the porous-medium equation and the Hele-Shaw problem
• Schrödinger operators with singular potentials
• On the Weak Solution of Moving Boundary Problems
• The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
• Remarks on the quasi-steady one phase Stefan problem
• The Ill-Posed Hele-Shaw Model and The Stefan Problem for Supercooled Water
• The Mesa Problem: Diffusion Patterns for u_t = ∇ · (u^m∇u) as m → +∞
• Continuity of the Density of a Gas Flow in a Porous Medium
• A variational inequality approach to Hele-Shaw flow with a moving boundary
• Limit behaviour of focusing solutions to nonlinear diffusions
• Convergence of the porous media equation to Hele-Shaw