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

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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

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

Abstract
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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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