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July  2009, 25(2): 545-565. doi: 10.3934/dcds.2009.25.545

A variational inequality in Bean's model for superconductors with displacement current

Frank Jochmann 1,

1. 

Technische Universität Berlin, Fakultät II - Mathematik und Naturwissenschaften, Institut für Mathematik, Strasse des 17. Juni 136, 10623 Berlin, Germany

Received  September 2008 Revised  January 2009 Published  June 2009

The paper deals with Bean's critical state model for the description of the electromagnetic field in superconductors. A variational inequality for the quasi-stationary approximation on a part of the spatial domain is given. The main goals are the existence, uniqueness and asymptotic behavior as $t\rightarrow\infty$ of the solutions to that system.
Keywords: Maxwell's equations, Bean's model, quasi-stationary limit, asymptotic behavior., initial-boundary-value problem.
Mathematics Subject Classification: Primary: 35Q60, 35D05; Secondary: 58E3.
Citation: Frank Jochmann. A variational inequality in Bean's model for superconductors with displacement current. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 545-565. doi: 10.3934/dcds.2009.25.545
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