A Cauchy integral approach to Hele-Shaw problems with a free boundary: The case of zero surface tension

DOI10.1007/BF02198454zbMath0860.35152OpenAlexW1981789388MaRDI QIDQ1817420

Fei-Ran Tian

Publication date: 6 January 1997

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02198454

zbMATH Keywords

regularityexistenceuniquenessclassical solutionsinverse propertiesanalytic initial boundariesCauchy integral of the free boundarynon-analytic initial boundaries

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) PDEs in connection with fluid mechanics (35Q35) Inverse problems for PDEs (35R30) Free boundary problems for PDEs (35R35)

Related Items

The Dirichlet problem for the complex homogeneous Monge-Ampère equation, Hele-Shaw flows with anisotropic surface tension, On diffusive slowdown in three-layer Hele-Shaw flows, The Hele-Shaw flow and moduli of holomorphic discs, Analytic solution to an interfacial flow with kinetic undercooling in a time-dependent gap Hele-Shaw cell, On the breakdown of Hele-Shaw solutions with nonzero surface tension, Exponential Transforms, Resultants and Moments

Cites Work

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• Applications of Variational Inequalities to a Moving Boundary Problem for Hele Shaw Flows
• Hele - Shaw flow and pattern formation in a time-dependent gap
• A Moment Problem on Jordan Domains
• Global solutions for small data to the Hele-Shaw problem
• Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel