All Time Smooth Solutions of the One-Phase Stefan Problem and the Hele-Shaw Flow

DOI10.1081/PDE-120028844zbMath1099.35175OpenAlexW1998550262MaRDI QIDQ3157883

Ki-Ahm Lee, Panagiota Daskalopoulos

Publication date: 20 January 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120028844

zbMATH Keywords

free boundaryHele-Shaw flowslog concavityStephan problem

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Free boundary problems for PDEs (35R35) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items (12)

Regularity of the free boundary for the one phase Hele--Shaw problem ⋮ Adaptive finite difference methods for nonlinear elliptic and parabolic partial differential equations with free boundaries ⋮ Global stability of steady states in the classical Stefan problem for general boundary shapes ⋮ Local Well-Posedness and Global Stability of the Two-Phase Stefan Problem ⋮ Regularity for a special case of two-phase Hele-Shaw flow via parabolic integro-differential equations ⋮ Power concavity on nonlinear parabolic flows ⋮ Parabolic approach to nonlinear elliptic eigenvalue problems ⋮ Long time regularity of solutions of the Hele--Shaw problem ⋮ The Hele-Shaw problem as a ‘‘Mesa” limit of Stefan problems: Existence, uniqueness, and regularity of the free boundary ⋮ The Stefan problem and concavity ⋮ Global Stability and Decay for the Classical Stefan Problem ⋮ Classical solvability of multidimensional two-phase Stefan problem for degenerate parabolic equations and Schauder's estimates for a degenerate parabolic problem with dynamic boundary conditions

Cites Work

• Classical solutions of the Stefan problem
• All time \(C^\infty\)-regularity of the interface in degenerate diffusion: A geometric approach
• ON THE CLASSICAL SOLUTION OF THE MULTIDIMENSIONAL STEFAN PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS
• Classical Solutions of Multidimensional Hele--Shaw Models
• Convexity properties of solutions to some classical variational problems
• Convexity and all‐time C^∞‐regularity of the interface in flame propagation

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