no. G7
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Uniqueness result for a weighted pendulum equation modeling domain walls in notched ferromagnetic nanowires
Ignat, Radu1
1 Institut de Mathématiques de Toulouse & Institut Universitaire de France, UMR 5219, Université de Toulouse, CNRS, UPS IMT, F-31062 Toulouse Cedex 9, France
Comptes Rendus. Mathématique, Tome 360 (2022) no. G7, pp. 819-828.

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.

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DOI : 10.5802/crmath.349
Ignat, Radu 1

1 Institut de Mathématiques de Toulouse & Institut Universitaire de France, UMR 5219, Université de Toulouse, CNRS, UPS IMT, F-31062 Toulouse Cedex 9, France 
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     title = {Uniqueness result for a weighted pendulum equation modeling domain walls in notched ferromagnetic nanowires},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {819--828},
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Ignat, Radu. Uniqueness result for a weighted pendulum equation modeling domain walls in notched ferromagnetic nanowires. Comptes Rendus. Mathématique, Tome 360 (2022) no. G7, pp. 819-828. doi : 10.5802/crmath.349. http://www.numdam.org/articles/10.5802/crmath.349/

[1] Carbou, Gilles; Labbé, Stéphane Stability for static walls in ferromagnetic nanowires, Discrete Contin. Dyn. Syst., Volume 6 (2006) no. 2, pp. 273-290 | MR | Zbl

[2] Carbou, Gilles; Sanchez, David Stabilization of walls in notched ferromagnetic nanowires (2018) (https://hal.archives-ouvertes.fr/hal-01810144)

[3] Côte, Raphaël; Ignat, Radu Asymptotic stability of precessing domain walls for the Landau–Lifshitz–Gilbert equation in a nanowire with Dzyaloshinskii-Moriya interaction (2022) (https://arxiv.org/abs/2202.01005)

[4] Döring, Lukas; Ignat, Radu; Otto, Felix A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types, J. Eur. Math. Soc., Volume 16 (2014) no. 7, pp. 1377-1422 | DOI | MR | Zbl

[5] Ignat, Radu; Moser, Roger Interaction energy of domain walls in a nonlocal Ginzburg–Landau type model from micromagnetics, Arch. Ration. Mech. Anal., Volume 221 (2016) no. 1, pp. 419-485 | DOI | MR | Zbl

[6] Ignat, Radu; Nguyen, Luc Local minimality of ℝ N -valued and 𝕊 N -valued Ginzburg–Landau vortex solutions in the unit ball B N (2021) (https://arxiv.org/abs/2111.07669)

[7] Ignat, Radu; Nguyen, Luc; Slastikov, Valeriy; Zarnescu, Arghir Stability of the melting hedgehog in the Landau–de Gennes theory of nematic liquid crystals, Arch. Ration. Mech. Anal., Volume 215 (2015) no. 2, pp. 633-673 | DOI | MR | Zbl

[8] Ignat, Radu; Nguyen, Luc; Slastikov, Valeriy; Zarnescu, Arghir On the uniqueness of minimisers of Ginzburg–Landau functionals, Ann. Sci. Éc. Norm. Supér., Volume 53 (2020) no. 3, pp. 589-613 | DOI | MR | Zbl

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