The Journal of Geometric Analysis

, 15:641

The one-phase Hele-Shaw problem with singularities

Article

DOI: 10.1007/BF02922248

Cite this article as:
Jerison, D. & Kim, I. J Geom Anal (2005) 15: 641. doi:10.1007/BF02922248

Abstract

In this article we analyze viscosity solutions of the one phase Hele-Shaw problem in the plane and the corresponding free boundaries near a singularity. We find, up to order of magnitude, the speed at which the free boundary moves starting from a wedge, cusp, or finger-type singularity. Maximum principle-type arguments play a key role in the analysis.

Math Subject Classifications

35K55

Key Words and Phrases

Free boundarysingularity analysisviscosity solutionsHele-Shaw flow

Copyright information

© Mathematica Josephina, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsMITUSA
  2. 2.Department of MathematicsUCLAUSA