Asymptotic behaviour of the solutions of an evolutionary Ginzburg-Landau superconductivity model. (English) Zbl 0845.35118

Liang, Jin; Qi, Tang

J. Math. Anal. Appl. 195, No. 1, 92-107 (1995).

Summary: The asymptotic behaviour of the solutions of a non-stationary Ginzburg-Landau superconductivity model is discussed. Under suitable choices of gauge, it is proved that, as \(t\) tends to infinity, the \(\omega\)-limit set of the solutions of the evolutionary superconductivity model consists of the solutions of the steady-state problem only. An example of non-convergence is also given for solutions under a particular choice of gauge.

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
82D55	Statistical mechanics of superconductors
78A35	Motion of charged particles
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

non-stationary Ginzburg-Landau superconductivity model; suitable choices of gauge; steady-state problem