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Asymptotic behaviour of time‐dependent Ginzburg–Landau equations of superconductivity
Author(s) -
RodriguezBernal Anibal,
Wang Bixiang,
Willie Robert
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199912)22:18<1647::aid-mma97>3.0.co;2-w
Subject(s) - attractor , mathematics , superconductivity , exponential growth , exponential function , mathematical physics , statistical physics , mathematical analysis , physics , quantum mechanics
In this paper, we establish the global fast dynamics for the time‐dependent Ginzburg–Landau equations of superconductivity. We show the squeezing property and the existence of finite‐dimensional exponential attractors for the system. In addition we prove the existence of the global attractor in L 2 × L 2 for the Ginzburg–Landau equations in two spatial dimensions. Copyright © 1999 John Wiley & Sons, Ltd.