A variational inequality inBean's model for superconductors with displacement current

Frank Jochmann

doi:10.3934/dcds.2009.25.545

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2009, Volume 25, Issue 2: 545-565. Doi: 10.3934/dcds.2009.25.545

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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

Received: August 31, 2008

Revised: December 31, 2008

Published: May 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q60, 35D05; Secondary: 58E35.

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