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Homogenization of Reynolds equation by two-scale convergence. (English) Zbl 1124.35007

Summary: To increase the hydrodynamic performance in different machine elements, as e.g. journal bearings and thrust bearings, during lubrication it is important to understand the influence of surface roughness. In this connection one encounters homogenization of the incompressible Reynolds equation, where the roughness of the lubricated surface is assumed to be periodic. This problem has recently been studied in more engineering-oriented papers by using the formal method of multiple scale expansion. In this paper, we rigorously prove both homogenization and corrector results by using two-scale convergence, which may be regarded as a justification of the formal multiple scale expansion method described above. Moreover, some numerical illustrations and results are presented.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
76D08 Lubrication theory
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References:

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