Convergence of the porous media equation to Hele-Shaw

DOI10.1016/S0362-546X(99)00325-9zbMath1016.35042OpenAlexW2087055512WikidataQ127633880 ScholiaQ127633880MaRDI QIDQ5940178

Fernando Quirós, Omar Gil

Publication date: 20 September 2001

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(99)00325-9

zbMATH Keywords

energy estimatescomparison theoremcompactly supported initial datalimiting equationmonotonicity results

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) A priori estimates in context of PDEs (35B45)

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Cites Work

• The relation between the porous medium and the eikonal equations in several space dimensions
• The porous medium equation as a finite-speed approximation to a Hamilton- Jacobi equation
• A singular limit problem for the porous medium equation
• Schrödinger operators with singular potentials
• Similarity profiles of flows through porous media
• 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 → +∞
• A variational inequality approach to Hele-Shaw flow with a moving boundary
• Limit behaviour of focusing solutions to nonlinear diffusions
• Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel
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