2015/04/03 by Mickaël Dos Santos, Santos, Mickaël Dos, Rémy Rodiac +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1504.00845
openalex publication_date 2015/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let D =Ω∖ω ⊂ ℝ2 be a smooth annular type domain. We consider the simplified Ginzburg-Landau energy Eε(u)=(1)/(2)∫D |∇ u|2 +(1)/(4ε2)∫D (1-|u|2)2, where u: D → ℂ, and look for minimizers of Eε with prescribed degrees deg(u,∂ Ω)=p, deg(u,∂ ω)=q on the boundaries of the domain. For large ε and for balanced degrees, i.e., p=q, we obtain existence of minimizers for \it thin domain. We also prove non-existence of minimizers of Eε, for large ε, in the case p≠ q, pq>0 and D is a circular annulus with large capacity (corresponding to "thin" annulus). Our approach relies on similar results obtained for the Dirichlet energy E_∞(u)=(1)/(2)∫D|∇ u|2, the existence result obtained by Berlyand and Golovaty and on a technique developed by Misiats.