Étude symbolique de la perte de régularité C ∞ par morceaux dans l'interaction d'ondes semi-linéaires

Abstract

We consider the interaction of two piecewise smooth waves for a first order semilinear system. We know that under geometric hypotheses the piecewise smooth regularity can be not conserved after the interaction. A symbolic study allows us to prove that this loss does not appear on principal singularities. We then show the microlocal mechanism of the creation and the propagation of a logarithmic singularity.