Analysis of a mean field model of superconducting vortices

1999 ◽  
Vol 10 (4) ◽  
pp. 319-352 ◽  
Author(s):  
R. SCHÄTZLE ◽  
V. STYLES
Keyword(s):  
Weak Solution ◽  
Steady State ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Field Model ◽  
Mean Field ◽  
Two Dimensions ◽  
Mean Field Model ◽  
Superconducting Vortices

We study a mean-field model of superconducting vortices in one and two dimensions. The existence of a weak solution and a steady-state solution of the model are proved. A special case of the steady-state problem is shown to be of the form of a free boundary problem. The solutions of this free boundary problem are investigated. It is also shown that the weak solution of the one-dimensional model is unique and satisfies an entropy inequality.

A mean-field model of superconducting vortices

1996 ◽  
Vol 7 (2) ◽  
pp. 97-111 ◽  
Author(s):  
S. J. Chapman ◽  
J. Rubinstein ◽  
M. Schatzman
Keyword(s):  
Steady State ◽  
Field Model ◽  
Local Existence ◽  
Mean Field ◽  
State Problem ◽  
Mean Field Model ◽  
Type Ii Superconductor ◽  
Superconducting Vortices ◽  
Steady State Problem ◽  
Steady State Solutions

A mean-field model for the motion of rectilinear vortices in the mixed state of a type-II superconductor is formulated. Steady-state solutions for some simple geometries are examined, and a local existence result is proved for an arbitrary smooth geometry. Finally, a variational formulation of the steady-state problem is given which shows the solution to be unique.

scholarly journals Existence of Weak Solution for a Free Boundary Lubrication Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Abdelhamid Laouar
Keyword(s):  
Weak Solution ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Boundary Lubrication ◽  
Hydrodynamic Lubrication ◽  
Weak Formulation ◽  
Large Context ◽  
A Free Boundary Problem

This paper is interested in a free boundary problem modelling a phenomenon of cavitation in hydrodynamic lubrication. We reformulate the problem (see Boukrouche, (1993)) in a large context by introducing two positive parameters, namely, N0 and a. We build a weak formulation and establish the existence of the solution to the problem.

Steady-state properties of a mean-field model of driven inelastic mixtures

2002 ◽  
Vol 66 (1) ◽  
Author(s):  
Umberto Marini Bettolo Marconi ◽  
Andrea Puglisi
Keyword(s):  
Steady State ◽  
Field Model ◽  
Mean Field ◽  
Mean Field Model
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