Ginzburg-Landau equation with magnetic effect in a thin domain |
| |
Authors: | Shuichi Jimbo Yoshihisa Morita |
| |
Institution: | (1) Department of Mathematics, Hokkaido University, Sapporo 060-0810 Japan (e-mail: jimbo@math.sci.hokudai.ac.jp) , JP;(2) Department of Applied Mathematics and Informatics, Ryukoku University, Seta Otsu 520-2194 Japan (e-mail: morita@rins.ryukoku.ac.jp) , JP |
| |
Abstract: | We study the Ginzburg-Landau equation with magnetic effect in a thin domain in , where the thickness of the domain is controlled by a parameter . This equation is an Euler equation of a free energy functional and it has trivial solutions that are minimizers of the functional.
In this article we look for a nontrivial stable solution to the equation, that is, a local minimizer of the energy functional.
To prove the existence of such a stable solution in , we consider a reduced problem as and a nondegenerate stable solution to the reduced equation. Applying the standard variational argument, we show that there
exists a stable solution in near the solution to the reduced equation if is sufficiently small. We also present a specific example of a domain which allows a stable vortex solution, that is, a stable
solution with zeros.
Received: 11 May 2001 / Accepted: 11 July 2001 /Published online: 19 October 2001 |
| |
Keywords: | Mathematics Subject Classification (2000): 35J20 35J50 35Q60 74K35 |
本文献已被 SpringerLink 等数据库收录! |
|