Homogenization of the Hele-Shaw Problem in Periodic Spatiotemporal Media

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 o...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2015-07, Vol.217 (1), p.155-230
Main Author: Pozar, Norbert
Format: Article
Language:English
Subjects:
Archives
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Free boundaries
Homogenization
Homogenizing
Mathematical and Computational Physics
Media
Nonlinearity
Physics
Physics and Astronomy
Theoretical
Viscosity
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Summary: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.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-014-0831-0