[ Contact me ]

Address:

Laboratoire de Mathématiques et de leurs application - Pau (UMR CNRS 5142)
Bâctiment IPRA - Université de Pau et des Pays de l'Adour
Avenue de l'Université - BP 1155
64013 PAU CEDEX
Phone: +33 (0)5 59 40 75 15
Fax: +33 (0)5 59 40 75 55
E-mail: mehdi.badra(@)univ-pau.fr

[ Current Position ]

I am currently Maître de conférences (assistant professor) at Université de Pau et des Pays de l'Adour. I am a member of Laboratoire de Mathématiques et de leurs Applications de Pau.

[ Research Interests ]

My research interests are mainly around control and stabilization issues for fluid systems. The key words of my main research issues are:

My work also concerns approximation issues for control problems, the well-posedness of degenerate and singular PDE and some identification problems for immersed body.

[ Projects ]

I am a member of  the Indo-French Center of Applied Mathematics reseach project Control of PDE coordinated by Mythily Ramaswamy and Sylvain Ervedoza. 

[ Publications ]

Papers in journals

  1. Local controllability to trajectories for non-homogeneous incompressible Navier-Stokes equations, M. Badra, S. Ervedoza and S. Guerrero, to appear in Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 33, n. 2, pp. 529—574, 2016.
  2. Feedback Stabilization of a Fluid-Rigid body Interaction System, M. Badra and T. Takahashi, Advances in Differential Equations, vol. 19, n. 11-12, pp. 1137—1184, 2014.
  3. On the Fattorini Criterion for Approximate Controllability and Stabilizability of Parabolic Systems, M. Badra and T. Takahashi, ESAIM: Control, Optimisation and Calculus of Variations, vol. 20, n. 3, pp. 924—956, 2014.
  4. Local Controllability to trajectories of the magnetohydrodynamic equations, M. Badra, Journal of  Mathematical Fluid Mechanics , vol. 16, n. 4, pp. 631—660, 2014.
  5. Feedback stabilization of a simplified 1d fluid--particle system, M. Badra and T. Takahashi, Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 31, n. 2, pp. 369—389, 2014.
  6. A singular parabolic equation: existence, stabilization, M. Badra, K. Bal and J. Giacomoni, Journal of Differential Equations, vol. 252, n. 9, pp. 5042—5075, 2012.
  7. Abstract settings for stabilization of nonlinear parabolic system with a Riccati-based strategy. Application to Navier-Stokes and Boussinesq equations with Neumann or Dirichlet control, M. Badra, Discrete and Continuous Dynamical Systems - Series A, vol. 252, n. 9, pp. 5042—5075, 2012.
  8. Méthode de pénalisation pour le contrôle frontière des équations de Navier-Stokes, M. Badra, J.-M. Buchot and L. Thevenet, Journal Européen des Systèmes Automatisés, vol. 45, numéro spécial Méthodes numériques et applications des systèmes à paramètres répartis, 2011.
  9. Some results about a quasilinear singular parabolic equation, M. Badra, K. Bal and J. Giacomoni, Differential Equations and Applications, vol. 3, n. 4, pp. 609-627, 2011.
  10. Global Carleman Inequalities for Stokes and Penalized Stokes Equations, M. Badra, Mathematical Control and Related Fields, vol. 1, n. 2, pp. 149—175, 2011.
  11. Existence Results to a quasilinear and singular parabolic equation, M. Badra, K. Bal and J. Giacomoni, Discrete and Continuous Dynamical Systems - Series A, Dynamical systems, differential equations and applications. 8th AIMS Conference. Suppl. Vol. I, pp. 117—125, 2011.
  12. Detecting an obstacle immersed in a fluid by shape optimization methods, M. Badra, F. Caubet and M. Dambrine, Mathematical Models and Methods in Applied Sciences, vol. 21, issue 10, pp. 2069—2101, 2011.
  13. Stabilization of parabolic nonlinear systems with finite dimensional feedback or dynamical controllers. Application to the Navier-Stokes system, M. Badra and T. Takahashi, SIAM Journal on Control and Optimization, vol. 49, pp. 420-463, 2011.
  14. Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system, M. Badra, ESAIM: Control, Optimisation and Calculus of Variations, vol. 15, n. 4, pp. 934—968, 2009.
  15. Lyapunov Function and Local Feedback Boundary Stabilization of the Navier-Stokes Equations, M. Badra, SIAM Journal on Control and Optimization , vol. 48, issue 3, pp. 1797-1830, 2009.
  16. Local stabilization of the Navier-Stokes System with a Feedback Controller Localized in an Open Subset of the Domain, M. Badra, Numerical Functional Analysis and Optimization, vol. 28, n. 5-6, pp. 559–589, 2007.

Proceedings

  1. Riccati-based strategies for feedback boundary stabilization of the 3D NavierStokes equations, M. Badra, 3rd International Conference on Approximation Methods and Numerical Modelling in Environment and Natural Resources , Pau, Volume 1, pp. 175-180, 2009.
  2. Feedback stabilization of the 3-D Navier-Stokes equations based on an extended system, M. Badra, IFIP Int. Fed. Inf. Process., Systems, control, modeling and optimization, 13–24, 2006. pp. 559–589, 2007.

Theses

  • HDR Thesis: The defence of my "habilitation à diriger des recherches" (HDR) took place Tuesday, December 10, 2013 (My HDR Thesis).
  • PHD Thesis: the defence of my Phd Thesis took place Tuesday, December 07, 2006 (My Phd Thesis).

[ Phd Students ]


[ CV ]

My detailed (french) CV in pdf format.