American Institute of Mathematical Sciences

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April  1998, 4(2): 205-224. doi: 10.3934/dcds.1998.4.205

Determining nodes for the Ginzburg-Landau equations of superconductivity

Hans G. Kaper 1, , Bixiang Wang 2, and  Shouhong Wang 3,

1. 

Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, United States
2. 

Department of Applied Mathematics, Tsinghua University, Beijing 100084, China
3. 

Department of Mathematics, Indiana University, Bloomington, IN 47405, United States

Received  September 1997 Published  February 1998

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.
Keywords: superconductivity, determining nodes., large-time asymptotic behavior, Ginzburg-Landau equations.
Mathematics Subject Classification: Primary: 35K57; Secondary: 35B40, 58F39, 82D5.
Citation: Hans G. Kaper, Bixiang Wang, Shouhong Wang. Determining nodes for the Ginzburg-Landau equations of superconductivity. Discrete & Continuous Dynamical Systems - A, 1998, 4 (2) : 205-224. doi: 10.3934/dcds.1998.4.205
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