Comptes Rendus
Partial differential equations
Uniqueness result for a weighted pendulum equation modeling domain walls in notched ferromagnetic nanowires
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 819-828.

We prove an existence and uniqueness result for solutions φ to a weighted pendulum equation in 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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.349
Radu Ignat 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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     author = {Radu Ignat},
     title = {Uniqueness result for a weighted pendulum equation modeling domain walls in notched ferromagnetic nanowires},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {819--828},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2022},
     doi = {10.5802/crmath.349},
     language = {en},
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Radu Ignat. Uniqueness result for a weighted pendulum equation modeling domain walls in notched ferromagnetic nanowires. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 819-828. doi : 10.5802/crmath.349. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.349/

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

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

[3] Raphaël Côte; Radu Ignat 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] Lukas Döring; Radu Ignat; Felix Otto 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] Radu Ignat; Roger Moser 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] Radu Ignat; Luc Nguyen Local minimality of N -valued and 𝕊 N -valued Ginzburg–Landau vortex solutions in the unit ball B N (2021) (https://arxiv.org/abs/2111.07669)

[7] Radu Ignat; Luc Nguyen; Valeriy Slastikov; Arghir Zarnescu 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] Radu Ignat; Luc Nguyen; Valeriy Slastikov; Arghir Zarnescu 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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