On the Cauchy problem for phase and vortices in the parabolic Ginzburg-Landau equation. (English) Zbl 1144.35399
Alama, Stanley (ed.) et al., Singularities in PDE and the calculus of variations. Selected papers of the CRM workshop, Montreal, Canada, July 17– 21, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4350-5/pbk). CRM Proceedings and Lecture Notes 44, 11-31 (2008).
Summary: The purpose of this note is twofold. Firstly, we survey some of our recent works concerning the dynamics of vortices in the two dimensional parabolic Ginzburg-Landau equation, emphasizing in particular the vortex-phase interaction. Secondly, we wish to supplement the analysis carried out in these work with a discussion on the initial value problem both for the vortices and the phase.
For the entire collection see [Zbl 1135.35003].
For the entire collection see [Zbl 1135.35003].
MSC:
| 35K55 | Nonlinear parabolic equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35Q40 | PDEs in connection with quantum mechanics |
| 35K15 | Initial value problems for second-order parabolic equations |
| 35B25 | Singular perturbations in context of PDEs |
| 35A15 | Variational methods applied to PDEs |
