Equipe EDP, Modélisation, Simulations

  • Themes  :
    • Partial differential equations (PDEs) and stochastic partial differential equations (SPDEs)
    • Variational techniques
    • Nonlinear Elliptic and Parabolic Partial Differential Equations, Nonlocal and Integro-Differential Equations, and their Numerical Analysis [B. Andreianov, G. Barles, Y. Belaud, M.-F. Bidaut-Véron, E. Chasseigne, J. Fabbri, Ch. Georgelin, L. Véron]
    • Analysis and Approximation of Conservation Laws [B. Andreianov, S. Cordier, C. Di Russo, F. James, C. Lucas, V. Perrollaz, M. Ribot, A. Sylla] : measure solutions for conservation equations, existence of solutions for coupled hyperbolic-parabolic PDEs systems, existence of solutions for quasi-geostrophic type models, well-balanced schemes for hyperbolic systems of PDEs, schemes for hyperbolic PDEs on networks, interface problems for conservation laws
    • Dispersive Equations [L. Molinet, V. Perrollaz]
    • Hamilton-Jacobi Equations and Deterministic Optimal Control Problems [G. Barles, E. Chasseigne, Ch. Georgelin]
    • Control of Partial Differential Equations [B. Andreianov, V. Perrollaz, K.-D. Phung]
    • Kinetic equations, population dynamics and applications [S. Cordier, S. Mancini]
    • Reaction-diffusion equations, mathematical ecology [F. Kuczma, S. Madec]
    • Image processing [M. Bergounioux, L. Delsol, T. Haberkorn, C. Louchet, C. Lucas] : variational techniques in collaboration with probability, statistics and optimization;   clinical magnetic resonance imaging, tomography, thermo- and photo-acoustic tomography
  • Application areas  :
    • Physics [F. James] : phase transition models
    • Aero-space industry  [T. Haberkorn], parternship with Airbus Defense & Space and CNES : optimal control for aero-space industry
    • Fluid mechanics and hydrology  [S. Cordier, F. James, C. Laguerre,  C. Lucas], partnership with INRA, IRD, INRIA : generalized shallow-water equations, modeling of soil erosion and sediment transport
    • Biology and medicine [M. Bergounioux, C. Di Russo, M. Grillot, P. Grillot, S. Madec, S. Mancini, M. Ribot, T. Phan] : cellular adhesion by cadherines, modeling of micro-algae biofilm for biofuel production, modeling of gut microbiota, image processing for biology, modeling the pulsatile secretion of GnRH neurons, spatial biological control of insects invasion
    • Traffic  [B. Andreianov, A. Sylla]: macroscopic modeling of pedestrian and vehicle dynamics
    • Economy [S. Cordier]