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Quasistatic droplets in randomly perforated domains. (English) Zbl 1315.35166
In this paper the authors study the Hele-Shaw problem in a randomly perforated domain with zero Neumann boundary conditions. By making use of the extending De Giorgi-Nash-Moser type estimates to perforated domains, the authors establish the almost sure non-degenerated growth of the solution near the free boundary, then show that the solutions and their free boundary converge uniformly to those corresponding to a homogeneous and anisotropic Hele-Shaw problem set, as the characteristic scale of the domain goes to zero.
Reviewer: Cheng He (Beijing)
MSC:
35Q35 PDEs in connection with fluid mechanics
76D27 Other free boundary flows; Hele-Shaw flows
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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