2004Fez conference on Differential Equations and Mechanics.
Electron. J. Diff. Eqns.,
Conference 11, 2004, pp. 135142.
On a nonlinear problem modelling states of thermal
equilibrium of superconductors
Mohammed El khomssi
Abstract:
Thermal equilibrium states of superconductors are governed
by the nonlinear problem
with boundary condition
. Here the domain
is an open
subset of
with smooth boundary.
The field
represents the thermal state, which we assume is in
. The state
models the superconductor's
state which is the unique physically meaningful solution.
In previous works, the superconductor domain is unidirectional
while in this paper we consider a domain with arbitrary
geometry. We obtain the following results:
A set of criteria that leads to uniqueness of a superconductor state,
a study of the existence of normal states and the number of them,
and optimal criteria when the geometric dimension is 1.
Published October 15, 2004.
Math Subject Classifications: 35J60, 34L30, 35Q99.
Key Words: Equilibrium states; nonlinear; thermal equilibrium; superconductors.
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Mohammed El Khomssi
UFR MDA Faculty of Sciences and Technology
Fez, Morocco
email: elkhomssi@fstf.ma 
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