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Homogenization of a fluid problem with a free boundary
Author(s) -
Schweizer Ben
Publication year - 2000
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/1097-0312(200009)53:9<1118::aid-cpa3>3.0.co;2-j
Subject(s) - mathematics , homogenization (climate) , mathematical analysis , free boundary problem , nonlinear system , boundary value problem , curvature , geometry , physics , biodiversity , ecology , quantum mechanics , biology
The stationary Stokes equations with a free boundary are studied in a perforated domain. The perforation consists of a periodic array of cylinders of size and distance O (ε). The free boundary is given as the graph of a function on a two‐dimensional perforated domain. We derive equations for the two‐scale limit of solutions. The limiting equation is a free boundary system. It involves a nonlinear eliptic operator corresponding to the nonlinear mean‐curvature expression in the original equations. Depending on the equation for the contact angle, the pressure is in general unbounded. © 2000 John Wiley & Sons, Inc.