Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Global attractors for phase-lock equations in superconductivity

Pages: 243 - 256, Volume 2, Issue 2, May 2002      doi:10.3934/dcdsb.2002.2.243

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Mei-Qin Zhan - Department of Mathematics & Statistics, University of North Florida, Jacksonville, FL 32224, United States (email)

Abstract: In previous article [18], we introduced a system of equations to model the superconductivity phenomena. We investigated its connection to Ginzburg-Landau equations and proved the existence and uniqueness of both weak and strong solutions. In this article, we study the dynamic behavior of solutions to the system and prove existence of global attractors and estimate their Hausdorff dimensions.

Keywords:  Ginzburg-Landau (TDGL) equations, global attractors, Hausdorff dimension, phase-lock equations.
Mathematics Subject Classification:  35B05, 35B30, 35B65.

Received: April 2001;      Revised: October 2001;      Available Online: February 2002.