scholarly journals On the existence and uniqueness of a weak solution of a nonsteady transient free-boundary problem in porous media

1991 ◽  
Vol 34 (1) ◽  
pp. 33-39
Author(s):  
Turgut Ozis
Keyword(s):  
Porous Media ◽  
Weak Solution ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Existence And Uniqueness

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.

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.

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