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Qualitative investigation of nonlinear differential equations describing infiltration of water

Xingbao Wu (1995)

Annales Polonici Mathematici

A nonlinear differential equation of the form (q(x)k(x)u')' = F(x,u,u') arising in models of infiltration of water is considered, together with the corresponding differential equation with a positive parameter λ, (q(x)k(x)u')' = λF(x,u,u'). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established.

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

S. J. Alvarez (1989)

Publicacions Matemàtiques

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.

Quando è possibile formare bolle in un fluido, e quando no

Epifanio G. Virga (1986)

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

Bubbles are formed in a fluid by inflating a liquid film with a gas in which the pressure π ^ ⁢ ( ν ) is a strictly decreasing function of the specific volume, unbounded as ν → 0 + . We show that, if π ^ ⁢ ( ν ) grows as fast or faster than ν - 2 / 3 as ν → 0 + , then there is at least one stable equilibrium configuration of any such bubble, no matter how much gas has been used to inflate it. On the other hand, if π ^ ⁢ ( ν ) grows as slowly or slower than ν - 1 / 3 as ν → 0 + , then any such bubble has no equilibrium configuration, when the amount of gas within...

Quantum Euler-Poisson systems: Existence of stationary states

Ansgar Jüngel, Hailiang Li (2004)

Archivum Mathematicum

A one-dimensional quantum Euler-Poisson system for semiconductors for the electron density and the electrostatic potential in bounded intervals is considered. The existence and uniqueness of strong solutions with positive electron density is shown for quite general (possibly non-convex or non-monotone) pressure-density functions under a “subsonic” condition, i.e. assuming sufficiently small current densities. The proof is based on a reformulation of the dispersive third-order equation for the electron...

Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II

David Gérard-Varet, Daniel Han-Kwan, Frédéric Rousset (2014)

Journal de l’École polytechnique — Mathématiques

In this paper, we study the quasineutral limit of the isothermal Euler-Poisson equation for ions, in a domain with boundary. This is a follow-up to our previous work [5], devoted to no-penetration as well as subsonic outflow boundary conditions. We focus here on the case of supersonic outflow velocities. The structure of the boundary layers and the stabilization mechanism are different.

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