Displaying similar documents to “Geometry of the free-sliding Bernoulli beam”

Qualitative properties of the free-boundary of the Reynolds equation in lubrication.

S. J. Alvarez (1989)

Publicacions Matemàtiques

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The hydrodynamic lubrication of a cylindrical bearing is governed by the Reynolds equation that must be satisfied by the pressure of lubricating oil. When cavitation occurrs we are carried to an elliptic free-boundary problem where the free-boundary separates the lubricated region from the cavited region. Some qualitative properties are obtained about the shape of the free-boundary as well as the localization of the cavited region.

Understanding singularitiesin free boundary problems

Xavier Ros-Oton, Joaquim Serra (2019)

Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana

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Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfacesor boundaries. The most classical example is the melting of ice to water (the Stefan problem). In this case, the freeboundary is the liquid-solid interface between ice and water. A central mathematical challenge in this context is to understand the regularity and singularities of free boundaries. In this paper we provide a gentle introduction to this topic by presenting some classical results...