Determining nodes for the Ginzburg-Landau equations of superconductivity

Hans G. Kaper; Bixiang Wang; Shouhong Wang

doi:10.3934/dcds.1998.4.205

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1998, Volume 4, Issue 2: 205-224. Doi: 10.3934/dcds.1998.4.205

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Determining nodes for the Ginzburg-Landau equations of superconductivity

1.
Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439
2.
Department of Applied Mathematics, Tsinghua University, Beijing 100084
3.
Department of Mathematics, Indiana University, Bloomington, IN 47405

Received: September 1997

Published: April 1998

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Abstract

It is shown that a solution of the time-independent Ginzburg-Landau equations of superconductivity is determined completely and exactly by its values at a finite but sufficiently dense set of determining nodes in the domain. If the applied magnetic field is time dependent and asymptotically stationary, the large-time asymptotic behavior of a solution of the time-dependent Ginzburg-Landau equations of superconductivity is determined similarly by its values at a finite set of determining nodes, whose positions may vary with time.

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Mathematics Subject Classification: Primary: 35K57; Secondary: 35B40, 58F39, 82D55.

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