The Hele-Shaw problem as a ‘‘Mesa” limit of Stefan problems: Existence, uniqueness, and regularity of the free boundary

DOI10.1090/S0002-9947-08-04764-8zbMath1162.76018arXivmath/0410131OpenAlexW2145836529MaRDI QIDQ3617613

Ivan Blank, Charles N. Moore, Marianne K. Korten

Publication date: 30 March 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410131

zbMATH Keywords

pointwise convergencesingular limitmushy region

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stefan problems, phase changes, etc. (80A22) Free boundary problems for PDEs (35R35) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items (3)

The Hele-Shaw asymptotics for mechanical models of tumor growth ⋮ A Hele-Shaw limit without monotonicity ⋮ Reifenberg flatness of free boundaries in obstacle problems with VMO ingredients

Cites Work

• The one-phase Hele-Shaw problem with singularities
• Regularity for solutions of the two-phase Stefan problem
• Intermediate Schauder estimates
• Continuity of weak solutions to certain singular parabolic equations
• Initial traces of solutions to a one-phase Stefan problem in an infinite strip
• The obstacle problem revisited
• On some singular limits of homogeneous semigroups
• Elliptic partial differential equations of second order
• The mesa-limit of the porous-medium equation and the Hele-Shaw problem
• Regularity of the free boundary for the one phase Hele--Shaw problem
• On the pointwise jump condition at the free boundary in the 1-phase Stefan problem
• All Time Smooth Solutions of the One-Phase Stefan Problem and the Hele-Shaw Flow
• Regularity of one-phase Stefan problem near Lipschitz initial data
• 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
• Classical Solutions of Multidimensional Hele--Shaw Models
• Sharp results for the regularity and stability of the free boundary in the obstacle problem
• Nonnegative solutions of ut = δ(u-1)+: Regularity and uniqueness for the cauchy problem
• Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: An application to a model of tumor growth
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