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- Functional analysis : two-scale convergence, homogenization.
- Modelization : hyperbolic problems, conservation laws, Vlasov models, Euler models, small parameter systems, micro-macro decomposition, anisotropic diffusion problems.
- Physics : magnetic confinement fusion, weakly compressible fluids, charged particles beams, miscible flows in porous media.
- Scientific computing and numerical analysis : finite volume scheme, semi-lagrangian schemes, asymptotic-preserving schemes, curvilinear coordinates schemes.