Reflection of Progressing Waves for Quasilinear Hyperbolic Systems

Abstract

It is proved that when a progressing wave described by conormal distribution for a quasilinear hyperbolic 2 × 2 system hits a solid wall transvenally, the reflected wave remains conormal. In contrast to the semilinear case, such conormal distributions had to be defined inductively to take into account of the fact that the relevant characteristic surfaces are not necessarily smooth. The argument involves a suitable coordinate change to reduce the problem to a simple form and an iterative induction on the tangential regularity of the solution as well as that of the characteristic surfaces at which the wave fronts are situated.