Homogenization of a class of nonlinear variational inequalities with applications in fluid film flow
ABSTRACT The authors consider the homogenization of a class of nonlinear variational inequalities, which include rapid oscillations
with respect to a parameter. The homogenization of the corresponding class of differential equations is also studied. The
results are applied to some models for the pressure in a thin fluid film fluid between two surfaces which are in relative
motion. This is an important problem in the lubrication theory. In particular, the analysis includes the effects of surface
roughness on both faces and the phenomenon of cavitation. Moreover, the fluid can be modeled as Newtonian or non-Newtonian
by using a Rabinowitsch fluid model.
KeywordsHomogenization–Two-scale convergence–Lubrication–Variational inequalities