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Archive for Rational Mechanics and Analysis

, Volume 217, Issue 1, pp 155–230 | Cite as

Homogenization of the Hele-Shaw Problem in Periodic Spatiotemporal Media

  • Norbert Požár
Article
  • 155 Downloads

Abstract

We consider the homogenization of the Hele-Shaw problem in periodic media that are inhomogeneous both in space and time. After extending the theory of viscosity solutions into this context, we show that the solutions of the inhomogeneous problem converge in the homogenization limit to the solution of a homogeneous Hele-Shaw-type problem with a general, possibly nonlinear dependence of the free boundary velocity on the gradient. Moreover, the free boundaries converge locally uniformly in Hausdorff distance.

Keywords

Free Boundary Viscosity Solution Boundary Data Hausdorff Distance Comparison Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan
  2. 2.Faculty of Mathematics and Physics,Institute of Science and EngineeringKanazawa UniversityKanazawaJapan

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