Gilles Carbou

Responsabilités

• Directeur du LMAP depuis le premier septembre 2018

• Responsable du master de mathématiques et applications jusqu'au premier septembre 2018

• Co-responsable du CMI Mathématiques et Informatique jusqu'au premier septembre 2018

Thèmes de recherche

1. Analyse des EDP
2. Méthodes asymptotiques : couches limites, couches minces, justification de modèles 1d ou 2d
3. Analyse de stabilité

Domaines d'application

1. Ferromagnétisme : équation de Landau-Lifschitz
2. Electromagnétisme : guides d'ondes, équations de Kerr-Debye
3. Mécanique des fluides : équations de Stokes et Navier Stokes, interface fluide-milieu poreux

Encadrement

Encadrements de thèses

Thèse d'Abdelkader Al Sayed (soutenance prévue fin décembre 2017)

Thèse de Romeissa Rachi (Début de thèse en novembre 2017)

Thèse de Mouna Kassan (début de thèse en septembre 2019)

Enseignements Niveau Licence

Equations différentielles (L2MATH)

Mesure et Intégration (L3MATH)

Calcul différentiel et géométrie (L3MATH)

Niveau Master

Introduction à la géométrie différentielle (M1MMS)

Outils pour l'analyse des EDP (M2MMS)

Méthodes asymptotiques (M2MMS)

Mise à niveau EDP (ead)

Publications

Publications de rang A

• A. Al Sayed, G. Carbou, Walls in infinite bent Ferromagnetic Nanowires, sous presse
• G. Carbou, R. Jizzini, Very Regular Solutions for the Landau-Lifschitz Equation with Electric Current. Chin. Ann. Math. Ser. B 39 (2018), no. 5, 889–916.
• 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.