2006/12/14 by Ayman Kachmar, Kachmar, Ayman
Computer Science · Engineering · Mathematics · Physics and Astronomy · #35B40 #35J25 #35Q55 #82D55 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 35J60 #Secondary 35J20 #Stability and Controllability of Differential Equations #math-ph #math.AP #math.MP #msc:35B40 #msc:35J20 #msc:35J25 #msc:35J60 #msc:35Q55 #msc:82D55
paper · pdf · doi:10.48550/arxiv.math-ph/0612042
33 pages (revised version)
openalex publication_date 2006/12/14 · arxiv created 2007/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a generalized Ginzburg-Landau equation that models a sample formed of a superconducting/normal junction and which is not submitted to an applied magnetic field. We prove the existence of a unique positive (and bounded) solution of this equation. In the particular case when the domain is the entire plane, we determine the explicit expression of the solution (and we find that it satisfies a Robin (de Gennes) boundary condition on the boundary of the superconducting side). Using the result of the entire plane, we determine for the case of general domains, the asymptotic behavior of the solution for large values of the Ginzburg-Landau parameter. The main tools are Hopf's Lemma, the Strong Maximum Principle, elliptic estimates and Agmon type estimates.