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

Radu Ignat

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

Classical Analysis and ODEs 2021-12-28 v1 Mathematical Physics Analysis of PDEs math.MP

Authors: Radu Ignat

Abstract

We prove an existence and uniqueness result for solutions $\varphi$ to a weighted pendulum equation in $\mathbb{R}$ where the weight is non-smooth and coercive. We also establish (in)stability results for $\varphi$ 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.

Keywords

weighted pendulum equation existence and uniqueness stability ferromagnetic nanowires domain walls notched geometry

Cite

@article{arxiv.2112.13358,
  title  = {Uniqueness result for a weighted pendulum equation modeling domain walls in notched ferromagnetic nanowires},
  author = {Radu Ignat},
  journal= {arXiv preprint arXiv:2112.13358},
  year   = {2021}
}

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