Gilles Carbou

Responsabilities

Head of the LMAP since september 2018

Research interests

Partial Differential Equations Analysis

Asymptotic Methods (thin layers, boundary layers)

Application areas:

1. Ferromagnetism : Landau-Lifschitz equation
2. Electromagnetism : waves guides, Kerr-Debye Equations
3. Fluid Mechanics :Stokes and Navier Stokes equations

Publications

Publications de rang A

• G. Carbou, Walker Regime for Walls in Ferromagnetic Nanotubes, Nonlinear Anal. Real World Appl. 41 (2018), 642–664.

• P. Angot, G. Carbou, V. Péron, Asymptotic Study for Stokes-Brinkman model with jump embedded transmission conditions, Asymptot. Anal. 96 (2016), no. 3-4, 223–249.

• G. Carbou, P. Fabrie, K. Santugini, Weak solutions to the Landau-Lifshitz-Maxwell system with nonlinear Neumann boundary conditions arising from surface energies, Electron. J. Differential Equations 2015, No. 55, 25 pp.

• G. Carbou, R. Jizzini, Domain walls dynamics in a nanowire subject to an electric current, J. Differential Equations 258 (2015), no. 8, 2941–2965.

• G. Carbou, Metastability of Walls Congurations in Ferromagnetic Nanowires, SIAM J. Math. Anal. 46 (2014), no. 1, 45–95.

• G. Carbou, Domain walls dynamics for one-dimensional models of ferromagnetic nanowire, Differential Integral Equations 26 (2013), no. 3-4, 201–236.

• G. Carbou, S. Labbé, Stabilization of Walls for Nano-Wires of Finite Length, ESAIM Control Optim. Calc. Var. 18 (2012), no. 1, 1–21.

• S. Agarwal, G. Carbou, S. Labbé, C. Prieur, Control of a network of magnetic ellipsoidal samples, Math. Control Relat. Fields 1 (2011), no. 2, 129–147.

• G. Carbou, M. Effendiev, P. Fabrie, Global weak solutions for the Landau-Lifschitz Equation with Magnetostriction, Math. Methods Appl. Sci. 34 (2011), no. 10, 1274–1288.

• G. Carbou, Stability of static walls for a three-dimensional model of ferromagnetic material. J. Math. Pures Appl. 93 (2010), no. 2, 183–203.

• G. Carbou, B. Hanouzet, Relaxation approximation of the Kerr model for the three-dimensional initial-boundary value problem. J. Hyperbolic Differ. Equ. 6 (2009), no. 3, 577–614.

• G. Carbou, M. Effendiev, P. Fabrie, Relaxed model for the hysteresis in micromagnetism, Proc. Roy. Soc. Edinbugh Sect. A 139 (2009) no. 4, 759–773.

• G. Carbou, S. Labbé, E. Trélat, Smooth control of nanowires by means of a magnetic field. Commun. Pure Appli. Anal. 8 (2009), no. 3, 871–879.

• G. Carbou, B. Hanouzet, R. Natalini, Semilinear Behavior for Totally Linearly Degenerate Hyperbolic Systems with Relaxation. J. Differential Equations 246 (2009), no. 1, 291–319.

• G. Carbou, Brinkmann model and double penalization method for the flow around a porous thin layer. J. Math. Fluid Mech. 10 (2008), no. 1, 126–158.

• G. Carbou, S. Labbé, E. Trélat, Control of travelling walls in a ferromagnetic nanowire. Discrete Contin. Dyn. Syst. Ser S 1 (2008), no. 1, 51–59.

• G. Carbou, B. Hanouzet, Relaxation Approximation of some Initial-Boundary Value Problem for p-Systems, Communications in Math. Sciences 5 (2007), no. 1, 187–203.

• G. Carbou, B. Hanouzet, Relaxation approximation of some nonlinear Maxwell initial-boundary value problem, Commun. Math. Sci. 4 (2006), no. 2, 331–344.

• G. Carbou, S. Labbé, Stability for Static wall in a ferromagnetic Nanowire, Discrete Contin. Dyn. Syst. Ser. B 6 (2006), no. 2, 273–290.

• G. Carbou, P. Fabrie, O. Guès, On the ferromagnetism equations in the non static case, Comm. Pure Appli. Anal. 3 (2004), no. 3, 367–393.

• G. Carbou, Penalization method for viscous incompressible flow around a porous thin layer, Nonlinear Anal. Real World Appl. 5 (2004) no. 5, 815–855.

• G. Carbou, P. Fabrie, Boundary layers for a penalisation method for incompressible flow, Adv. Differential Equations 8 (2003), no. 12, 1453–1480.

• G. Carbou, P. Fabrie, O. Guès, Couche limite en ferromagnetisme, Comm. Partial Differential Equations 27 (2002), no. 7-8, 1467–1495.

• V. Bruneau, G. Carbou, Spectral asymptotic in Large Limit Coupling, Asymptot. Anal. 29 (2002), no. 2, 91–113.

• G. Carbou, Thin layers in Micromagnetism, Math. Models and Meth. in Applied Sciences 11 (2001), 1529–1546.

• G. Carbou, P. Fabrie, Regular Solutions for Landau-Lifschitz equations in R^3, Commun. Appl. Anal. 5 (2001), no.1, 17–30.

• G. Carbou, P. Fabrie, Regular Solutions for Landau-Lifschitz equations in a bounded domain, Differential Integral Equations 14 (2001), 213–229.

• G. Carbou, P. Fabrie, Time Average in Micromagnetism, J. Differential Equations 147 (1998), 383–409.

• G. Carbou, Regularity for critical points of a non local energy, Calculus of Variations 5 (1997), 409–433.

• G. Carbou, Unicité et minimalité des solutions d'une équation de Ginzburg-Landau, Ann. Inst. Henri Poincaré, Analyse non linéaire 3 (1995), 305–318.

• G. Carbou, Regularity for a non linear variational problem in dimension two, Manuscripta math. 78 (1993), 37–56.

 Lettres ou notes

• G. Carbou, B. Hanouzet, Comportement semi-linéaire d'un système hyperbolique quasi-linéaire : le modèle de Kerr-Debye, C.R. Acad. Sci. Paris Ser. I Math. 343 (2006), 243–247.

• G. Carbou, P. Fabrie, F. Jochmann, A remark on the Weak omega-Limit Set for Micromagnetism Equation, Applied Math. Letters 15 (2002), 95–99.

• G. Carbou, Modèle quasi-stationnaire en micromagnétisme, C. R. Acad. Sci. Paris Ser. I Math. 325 (1997), no. 8, 847–850.

• G. Carbou, P. Fabrie,  Comportement asymptotique des solutions faibles des équations de Landau-Lifschitz, C. R. Acad. Sci. Paris Ser. I Math. 325 (1997), no. 7, 717–720.

• G. Carbou, Applications harmoniques à valeurs dans un cercle, C. R. Acad. Sci. Paris Ser. I Math. 314 (1992), no. 5, 359–362.

Actes de congrès

• G. Carbou, B. Hanouzet, Relaxation Approximation of the Kerr-Debye Model for the Impedance Initial-Boundary Value Problem, Discrete Contin. Dyn. Syst. Supplement (2007), 212–220.

• G. Carbou, S. Labbé, Stability for walls in Ferromagnetic Nanowire, Numerical Mathematics and Advanced Application, Proceedings of Enumath 2005, Santiago de Compostela, Spain, July 2005, Springer.

• G. Carbou, P. Fabrie, O. Guès, Boundary Layers for Landau-Lifschitz Equations, Physica B, 343 (2004) 331–336 (actes du congrès Hysteresis and Micromagnetism Modeling, Salamanca 2003).

• G. Carbou, P. Fabrie, Recent results in micromagnetism, International Conference on Diff erential Equations, Vol. 1, 2 (Berlin, 1999), 738–740.