Displaying similar documents to “Boundary layer formation in the transition from the porous media equation to a Hele–Shaw flow”

A zoology of boundary layers.

David Gérard-Varet, Emmanuel Grenier (2002)

RACSAM

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In meteorology and magnetohydrodynamics many different boundary layers appear. Some of them are already mathematically well known, like Ekman or Hartmann layers. Others remain unstudied, and can be much more complex. The aim of this paper is to give a simple and unified presentation of the main boundary layers, and to propose a simple method to derive their sizes and equations.

Weak solutions for a well-posed Hele-Shaw problem

S. N. Antontsev, A. M. Meirmanov, V. V. Yurinsky (2004)

Bollettino dell'Unione Matematica Italiana

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We analyze existence and uniqueness of weak solutions to the well-posed Hele-Shaw problem under general conditions on the fixed boundaries and non-homogeneous governing equation in the unknown domain and non-homogeneous dynamic condition on the free boundary. Our approach allows us also to minimize the restrictions on the boundary and initial data. We derive several estimates on the solutions in B ⁢ V spaces, prove a comparison theorem, and show that the solution depends continuously on...

Recent results on the Boltzmann equation

Carlo Cercignani (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In the last few years the theory of the nonlinear Boltzmann equation has witnessed a veritable turrent of contributions, spurred by the basic result of DiPerna and Lions. Here we wish to survey these results with particular attention to some recent developments.