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Existence of solutions for elastohydrodynamic piezoviscous lubrication problems with a new model of cavitation. (English) Zbl 0856.76013
Summary: The purpose is to study a mathematical model of lubricating flow between elastic surfaces obeying the linear Hertzian theory when cavitation takes place. Cavitation is a free boundary phenomenon that is described in this paper by the Elrod-Adams model. This model introduces the concentration of fluid as well as the pressure as unknown functions; we suggest the model in preference to the classical variational inequality due to its ability to describe inflow and outflow. This leads to a nonlinear variational nonlocal equation. Herein, an existence theorem is proved by means of two different techniques.

MSC:
76D08 Lubrication theory
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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