Long-time behavior of a Hele-Shaw type problem in random media | Zendy

Norbert Požár | Zendy

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Long-time behavior of a Hele-Shaw type problem in random media

Author(s) -

Norbert Požár

Publication year - 2011

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/263

Subject(s) - type (biology) , hele shaw flow , mathematics , computer science , geology , flow (mathematics) , geometry , paleontology , open channel flow

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

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