May  2009, 8(3): 871-879. doi: 10.3934/cpaa.2009.8.871

Smooth control of nanowires by means of a magnetic field

1. 

MAB, UMR 5466, CNRS, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence cedex

2. 

Université Joseph Fourier, Laboratoire Jean Kuntzmann, CNRS, UMR 5224, 51 rue des Mathématiques, B.P. 53, 38041 Grenoble Cedex 9, France

3. 

Université d’Orléans, UFR Sciences, Fédération Denis Poisson Mathématiques, Laboratoire MAPMO, UMR 6628, Route de Chartres, BP 6759, 45067 Orléans Cedex 2

Received  June 2008 Revised  November 2008 Published  February 2009

We address the problem of control of the magnetic moment in a ferromagnetic nanowire by means of a magnetic field. Based on theoretical results for the 1D Landau-Lifschitz equation, we show a robust controllability result.
Citation: Gilles Carbou, Stéphane Labbé, Emmanuel Trélat. Smooth control of nanowires by means of a magnetic field. Communications on Pure and Applied Analysis, 2009, 8 (3) : 871-879. doi: 10.3934/cpaa.2009.8.871
[1]

Gaël Bonithon. Landau-Lifschitz-Gilbert equation with applied eletric current. Conference Publications, 2007, 2007 (Special) : 138-144. doi: 10.3934/proc.2007.2007.138

[2]

Behzad Azmi, Karl Kunisch. Receding horizon control for the stabilization of the wave equation. Discrete and Continuous Dynamical Systems, 2018, 38 (2) : 449-484. doi: 10.3934/dcds.2018021

[3]

Thierry Goudon, Frédéric Lagoutière, Léon M. Tine. The Lifschitz-Slyozov equation with space-diffusion of monomers. Kinetic and Related Models, 2012, 5 (2) : 325-355. doi: 10.3934/krm.2012.5.325

[4]

Xiaorui Wang, Genqi Xu. Uniform stabilization of a wave equation with partial Dirichlet delayed control. Evolution Equations and Control Theory, 2020, 9 (2) : 509-533. doi: 10.3934/eect.2020022

[5]

Andrei Fursikov, Lyubov Shatina. Nonlocal stabilization by starting control of the normal equation generated by Helmholtz system. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1187-1242. doi: 10.3934/dcds.2018050

[6]

Zhiling Guo, Shugen Chai. Exponential stabilization of the problem of transmission of wave equation with linear dynamical feedback control. Evolution Equations and Control Theory, 2022  doi: 10.3934/eect.2022001

[7]

Evelyne Miot, Mario Pulvirenti, Chiara Saffirio. On the Kac model for the Landau equation. Kinetic and Related Models, 2011, 4 (1) : 333-344. doi: 10.3934/krm.2011.4.333

[8]

D. Blömker, S. Maier-Paape, G. Schneider. The stochastic Landau equation as an amplitude equation. Discrete and Continuous Dynamical Systems - B, 2001, 1 (4) : 527-541. doi: 10.3934/dcdsb.2001.1.527

[9]

Xiaorui Wang, Genqi Xu, Hao Chen. Uniform stabilization of 1-D Schrödinger equation with internal difference-type control. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6359-6376. doi: 10.3934/dcdsb.2021022

[10]

Sorin Micu, Jaime H. Ortega, Lionel Rosier, Bing-Yu Zhang. Control and stabilization of a family of Boussinesq systems. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 273-313. doi: 10.3934/dcds.2009.24.273

[11]

Kay Kirkpatrick. Rigorous derivation of the Landau equation in the weak coupling limit. Communications on Pure and Applied Analysis, 2009, 8 (6) : 1895-1916. doi: 10.3934/cpaa.2009.8.1895

[12]

Immanuel Ben Porat. Local conditional regularity for the Landau equation with Coulomb potential. Kinetic and Related Models, , () : -. doi: 10.3934/krm.2022010

[13]

Andrei Fursikov. Stabilization of the simplest normal parabolic equation. Communications on Pure and Applied Analysis, 2014, 13 (5) : 1815-1854. doi: 10.3934/cpaa.2014.13.1815

[14]

Rohit Gupta, Farhad Jafari, Robert J. Kipka, Boris S. Mordukhovich. Linear openness and feedback stabilization of nonlinear control systems. Discrete and Continuous Dynamical Systems - S, 2018, 11 (6) : 1103-1119. doi: 10.3934/dcdss.2018063

[15]

Elena Braverman, Alexandra Rodkina. Stabilization of difference equations with noisy proportional feedback control. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2067-2088. doi: 10.3934/dcdsb.2017085

[16]

Serge Nicaise. Control and stabilization of 2 × 2 hyperbolic systems on graphs. Mathematical Control and Related Fields, 2017, 7 (1) : 53-72. doi: 10.3934/mcrf.2017004

[17]

Zuowei Cai, Jianhua Huang, Liu Yang, Lihong Huang. Periodicity and stabilization control of the delayed Filippov system with perturbation. Discrete and Continuous Dynamical Systems - B, 2020, 25 (4) : 1439-1467. doi: 10.3934/dcdsb.2019235

[18]

José R. Quintero, Alex M. Montes. On the exact controllability and the stabilization for the Benney-Luke equation. Mathematical Control and Related Fields, 2020, 10 (2) : 275-304. doi: 10.3934/mcrf.2019039

[19]

Kim Dang Phung. Boundary stabilization for the wave equation in a bounded cylindrical domain. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 1057-1093. doi: 10.3934/dcds.2008.20.1057

[20]

Wasim Akram, Debanjana Mitra. Local stabilization of viscous Burgers equation with memory. Evolution Equations and Control Theory, 2022, 11 (3) : 939-973. doi: 10.3934/eect.2021032

2020 Impact Factor: 1.916

Metrics

  • PDF downloads (89)
  • HTML views (0)
  • Cited by (5)

[Back to Top]