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This text contains a series of self-contained reviews on the state of the art in different areas of partial differential equations, presented by French mathematicians. Topics include qualitative properties of reaction-diffusion equations, multiscale methods coupling atomistic and continuum mechanics, adaptive semi-Lagrangian schemes for the Vlasov-Poisson equation, and coupling of scalar conservation laws.

Differential equations, Partial. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Partial differential equations --- Conservation Laws. --- Modelling. --- Numerical Analysis. --- Partial Differential Equations. --- Schroedinger Equation.