Uniqueness result for a weighted pendulum equation modeling domain walls in notched ferromagnetic nanowires

2021/12/26 by Radu Ignat, Ignat, Radu
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.CA #math.MP

paper · pdf · doi:10.48550/arxiv.2112.13358

arxiv created 2021/12/26 · arxiv updated 2021/12/28

Abstract

We prove an existence and uniqueness result for solutions φ to a weighted pendulum equation in ℝ where the weight is non-smooth and coercive. We also establish (in)stability results for φ according to the monotonicity of the weight. These results are applied in a reduced model for thin ferromagnetic nanowires with notches to obtain existence, uniqueness and stability of domain walls connecting two opposite directions of the magnetization.

Related

• Existence and Uniqueness of Domain Walls for Notched Ferromagnetic Nanowires
• Existence of travelling-wave solutions representing domain wall motion in a thin ferromagnetic nanowire
• Existence and the stability of minimizers in ferromagnetic nanowires
• On the stationary solution of the Landau-Lifshitz-Gilbert equation on a nanowire with constant external magnetic field
• Analytic form of head-to-head domain walls in thin ferromagnetic cylinders