Local and global existence results for anisotropic Hele–Shaw flows

DOI10.1017/S0308210500021351zbMath0922.76150MaRDI QIDQ4244015

Charles M. Elliott, Klaus Deckelnick

Publication date: 24 May 1999

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

moving boundary problemasymptotic behaviourregularization techniquetwo-phase Hele-Shaw flow

Mathematics Subject Classification ID

Incompressible viscous fluids (76D99) Free boundary problems for PDEs (35R35)

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Cites Work

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• The Hele--Shaw problem and area-preserving curve-shortening motions
• Évolution d'une interface par capillarité et diffusion de volume. I: Existence locale en temps
• A simplified proof for a moving boundary problem for Hele-Shaw flows in the plane
• Applications of Variational Inequalities to a Moving Boundary Problem for Hele Shaw Flows
• The Ill-Posed Hele-Shaw Model and The Stefan Problem for Supercooled Water
• Viscous fingering in Hele-Shaw cells
• A variational inequality approach to Hele-Shaw flow with a moving boundary
• Elliptic Partial Differential Equations of Second Order
• Existance uniqueness and regularity of classical solutions of the mullins—sekerka problem
• Classical Solutions of Multidimensional Hele--Shaw Models
• On classical solvability for the Hele-Shaw moving boundary problems with kinetic undercooling regularization
• Global solutions for small data to the Hele-Shaw problem

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