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1998, Volume 4, Issue 2: 205-224. Doi: 10.3934/dcds.1998.4.205
This issue Previous Article On the global existence of a cross-diffusion system Next Article Exponential attractors for nonautonomous first-order evolution equations

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
Abstract Related Papers Cited by
    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.
    Mathematics Subject Classification: Primary: 35K57; Secondary: 35B40, 58F39, 82D55.

    Citation:
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