Boletín SEMA, No 39 (2007)

Tamaño de la letra:  Pequeña  Mediana  Grande

A SURVEY ON MATHEMATICAL ASPECTS OF LUBRICATION PROBLEMS

G. Bayada, C. Vázquez

Resumen


In this paper a review concerning the main ideas, seminal papers and more recent advances in mathematica modelling of a wide class of lubrication problems is presented. After introducing the main ideas about different topics related to lubrication problems (thin film approximation, cavitation, rough surfaces ,elastohydrodynamc models, etc) and their mathematical translations, the authors mainly focus on the state of art (recent advances and open problems) in passing to the limit from more general Stokes equations to asymptotic Reynolds-like models. Finally, some comments on inverse problems and their related optimization formulations are also included.

Key words: tribology, lubrication, Stokes equation, Reynolds equation, cavitation ,free boundaries, homogenization, elastohydrodynamics, non Newtonian fluids, inverse problems, numerical methods.

AMS subject classifications: 76D08, 76A20, 74F10, 35R35, 35B27, 35J60, 35J85

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