  In this paper we continue the analysis of non-diagonalisable hyperbolic
systems initiated in \cite{GarJRuz, GarJRuz2}. Here we assume that the system
has discontinuous coefficients or more in general distributional coefficients.
Well-posedness is proven in the very weak sense for systems with singularities
with respect to the space variable or the time variable. Consistency with the
classical theory is proven in the case of smooth coefficients.

Analysis of PDEs