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