EDP, modélisation, simulation

Team animators: Pierre GABRIEL (Tours) & Bruno GALERNE (Orléans)

• 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, Ch. Georgelin, M. Grillot, 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, C. Carrère, E. Chasseigne, P. Gabriel, Ch. Georgelin, G. Nadin, V. Perrollaz]
  • Control of Partial Differential Equations [B. Andreianov, V. Perrollaz, K.-D. Phung]
  • Reaction-Diffusion Equations [C. Carrère, S. Madec, G. Nadin]: propagation and coexistence phenomena
  • 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, Related Models in Population Dynamics [J. Barré, S. Cordier, P. Gabriel, S. Mancini, G. Nadin]
  • Bifurcations, Slow-Fast Dynamics [S. Madec]
  • Positive Operators and Semigroups [P. Gabriel, G. Nadin]: principal eigenvalue problem, Doeblin-Harris techniques
  • 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. Carrère, 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, ecology, quantitative genetics, protein aggregation and neurodegenerative diseases, cell biology, cancer, neurosciences
  • 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]