EDP, modélisation, simulation

Team animators: Pierre GABRIEL & Bruno GALERNE

• Themes:
  • Partial differential equations (PDEs) and stochastic partial differential equations (SPDEs)
  • 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, P. Gabriel, Ch. Georgelin, G. Nadin, L. Véron]
    
  • Analysis and Approximation of Conservation Laws [B. Andreianov, S. Cordier, F. James, C. Lucas, V. Perrollaz, M. Ribot] : 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, P. Gabriel, Ch. Georgelin, G. Nadin]
  • Control of Partial Differential Equations [B. Andreianov, V. Perrollaz, K.-D. Phung]
  • Reaction-diffusion equations, mathematical ecology [P. Gabriel, S. Madec, G. Nadin]
  • Image processing [B. Galerne, 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
  • Kinetic equations, population dynamics and applications [J. Barré, S. Cordier, P. Gabriel, S. Mancini, G. Nadin]
  • Variational techniques

• Application areas:
  • Fluid mechanics and hydrology  [S. Cordier, F. James, M. Mancini,  C. Lucas], partnership with INRA, IRD, INRIA : generalized shallow-water equations, modeling of soil erosion and sediment transport
  • Biology and medicine [C. Georgelin, M. Grillot, P. Gabriel, P. Grillot, S. Madec, S. Mancini, G. Nadin, M. Ribot] : 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, epidemiology
  • Aero-space industry  [T. Haberkorn], parternship with Airbus Defense & Space and CNES : optimal control for aero-space industry
  • Traffic  [B. Andreianov]: macroscopic modeling of pedestrian and vehicle dynamics
  • Physics [J. Barré, F. James] : phase transition models, statistical mechanics
  • Economy [S. Cordier]