Stabilization of walls for nano-wires of finite length
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 1, pp. 1-21.

In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.

DOI : https://doi.org/10.1051/cocv/2010048
Classification : 35B35,  35K55
Mots clés : Landau-Lifschitz equation, control, stabilization
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     author = {Carbou, Gilles and Labb\'e, St\'ephane},
     title = {Stabilization of walls for nano-wires of finite length},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1--21},
     publisher = {EDP-Sciences},
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     url = {http://www.numdam.org/articles/10.1051/cocv/2010048/}
}
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Carbou, Gilles; Labbé, Stéphane. Stabilization of walls for nano-wires of finite length. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 1, pp. 1-21. doi : 10.1051/cocv/2010048. http://www.numdam.org/articles/10.1051/cocv/2010048/

[1] F. Alouges, T. Rivière and S. Serfaty, Néel and cross-tie wall energies for planar micromagnetic configurations. ESAIM : COCV 8 (2002) 31-68. | Numdam | MR 1932944 | Zbl 1092.82047

[2] W.F. Brown, Micromagnetics. Interscience Publisher, John Willey and Sons, New York (1963).

[3] G. Carbou, Regularity for critical points of a nonlocal energy. Calc. Var. 5 (1997) 409-433. | MR 1459796 | Zbl 0889.58022

[4] G. Carbou, Thin layers in micromagnetism. Math. Models Methods Appl. Sci. 11 (2001) 1529-1546. | MR 1872680 | Zbl 1012.82031

[5] G. Carbou and P. Fabrie, Time average in micromagnetism. J. Differ. Equ. 147 (1998) 383-409. | MR 1633953 | Zbl 0931.35170

[6] G. Carbou and P. Fabrie, Regular solutions for Landau-Lifschitz equation in a bounded domain. Differential Integral Equations 14 (2001) 213-229. | MR 1797387 | Zbl 1161.35421

[7] G. Carbou and P. Fabrie, Regular solutions for Landau-Lifschitz equation in R3. Commun. Appl. Anal. 5 (2001) 17-30. | MR 1844668 | Zbl 1084.35519

[8] G. Carbou and S. Labbé, Stability for static walls in ferromagnetic nanowires. Discrete Continous Dyn. Syst. Ser. B 6 (2006) 273-290. | MR 2176293 | Zbl 1220.82163

[9] G. Carbou, S. Labbé and E. Trélat, Control of travelling walls in a ferromagnetic nanowire. Discrete Contin. Dyn. Syst. Ser. S 1 (2008) 51-59. | MR 2375581

[10] A. Desimone, R.V. Kohn, S. Müller and F. Otto, Magnetic microstructures - a paradigm of multiscale problems, in ICIAM 99 (Edinburgh), Oxford Univ. Press, Oxford (2000) 175-190. | Zbl 0991.82038

[11] L. Halpern and S. Labbé, Modélisation et simulation du comportement des matériaux ferromagnétiques. Matapli 66 (2001) 70-86.

[12] T. Kapitula, Multidimensional stability of planar travelling waves. Trans. Amer. Math. Soc. 349 (1997) 257-269. | MR 1360225 | Zbl 0866.35021

[13] K. Kühn, Travelling waves with a singularity in magnetic nanowires. Commun. Partial Diff. Equ. 34 (2009) 722-764. | MR 2560299 | Zbl 1178.82086

[14] S. Labbé, Simulation numérique du comportement hyperfréquence des matériaux ferromagnétiques. Thèse de l'Université Paris 13, Paris (1998).

[15] S. Labbé and P.-Y. Bertin, Microwave polarisability of ferrite particles with non-uniform magnetization. J. Magn. Magn. Mater. 206 (1999) 93-105.

[16] T. Rivière and S. Serfaty, Compactness, kinetic formulation, and entropies for a problem related to micromagnetics. Commun. Partial Diff. Equ. 28 (2003) 249-269. | MR 1974456 | Zbl 1094.35125

[17] D. Sanchez, Méthodes asymptotiques en ferromagnétisme. Thèse de l'Université Bordeaux 1, Bordeaux (2004).

[18] A. Thiaville, J.M. Garcia and J. Miltat, Domain wall dynamics in nanowires. J. Magn. Magn. Mater. 242-245 (2002) 1061-1063.

[19] A. Visintin, On Landau Lifschitz equation for ferromagnetism. Japan Journal of Applied Mathematics 1 (1985) 69-84. | Zbl 0613.35018

[20] H. Wynled, Ferromagnetism, Encyclopedia of Physics XVIII/2. Springer-Verlag, Berlin (1966).

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