Self-similar focusing in porous media: An explicit calculation

D. G. Aronson

doi:10.3934/dcdsb.2012.17.1685

Article Contents

2012, Volume 17, Issue 6: 1685-1691. Doi: 10.3934/dcdsb.2012.17.1685

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Self-similar focusing in porous media: An explicit calculation

D. G. Aronson^1,

1.
Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455

Received: October 2010

Revised: December 2011

Published: September 2012

Abstract / Introduction Related Papers Cited by

Abstract

We consider a porous medium flow in which the material is initially distributed in the exterior of an empty region (a hole) and study the final stage of the hole-filling process as well as the initial stage of the post filling regime. It is known that in axially symmetric flow the hole-filling is asymptotically described by a self-similar solution which depends on a constant determined by the initial distribution. The post filling accumulation process is also locally described by a self-similar solution which in turn is characterized by a constant. In general, these constants must be found either experimentally or numerically. Here we present an example of a one-dimensional flow where the constants are obtained explicitly.

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Mathematics Subject Classification: Primary: 35K55, 76S05; Secondary: 35K15.

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References

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