Geodesic
Long-time behavior of a Hele-Shaw type problem in random media
Norbert Požár1 orcid
1UCLA, Los Angeles, USA
Interfaces and free boundaries, Tome 13 (2011) no. 3, pp. 373-395

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DOI

We study the long-time behavior of an exterior Hele–Shaw problem in random media with a free boundary velocity that depends on the position in dimensions n≥2. A natural rescaling of solutions that is compatible with the evolution of the free boundary leads to the homogenization of the free boundary velocity. By studying a limit obstacle problem for a Hele–Shaw problem with a point source, we are able to show the uniform convergence of the rescaled solution to a self-similar limit profile and we deduce that the rescaled free boundary uniformly approaches a sphere.
DOI : 10.4171/ifb/263
Classification : 00-XX

Norbert Požár  1

1 UCLA, Los Angeles, USA 
Norbert Požár. Long-time behavior of a Hele-Shaw type problem in random media. Interfaces and free boundaries, Tome 13 (2011) no. 3, pp. 373-395. doi: 10.4171/ifb/263
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     author = {Norbert Po\v{z}\'ar},
     title = {Long-time behavior of a {Hele-Shaw} type problem in random media},
     journal = {Interfaces and free boundaries},
     pages = {373--395},
     year = {2011},
     volume = {13},
     number = {3},
     doi = {10.4171/ifb/263},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/263/}
}
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