Propagation de singularités pour des problèmes aux limites d'ordre 2
In this paper, we prove propagation estimates for a massive Dirac equation in flat spacetime. This allows us to construct the asymptotic velocity operator and to analyse its spectrum. Eventually, using this new information, we are able to obtain complete scattering results; that is to say we prove the existence and the asymptotic completeness of the Dollard modified wave operators.
We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations.
We investigate the propagation of the uniform spatial Gevrey , σ ≥ 1, regularity for t → +∞ of solutions to evolution equations like generalizations of the Euler equation and the semilinear Schrödinger equation with polynomial nonlinearities. The proofs are based on direct iterative arguments and nonlinear Gevrey estimates.