Pinning with a variable magnetic field of the two dimensional Ginzburg–Landau model. (July 2016)

• Record Type: Journal Article
• Authors: Attar, Kamel
• Is Part Of: Nonlinear analysis. Volume 139(2016)
• Page Start: 1
• Page End: 54
• Publication Date: 2016-07
• Subjects: Magnetic Schrödinger operator -- Spectral theory -- Semi-classical analysis -- Ginzburg–Landau functional with variable magnetic field -- Pinning effect -- Superconducting; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.02.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the Ginzburg–Landau energy of a superconductor with a variable magnetic field and a pinning term in a bounded smooth two dimensional domain Ω . Supposing that the Ginzburg–Landau parameter and the intensity of the magnetic field are large and of the same order, we determine an accurate asymptotic formula for the minimizing energy. This asymptotic formula displays the influence of the pinning term. Also, we discuss the existence of non-trivial solutions and prove some asymptotics of the third critical field.