Anomalous singularities of semilinear non strictly hyperbolic systems (Q1263737)

The propagation of singularities of the solution of the Cauchy problem for semilinear nonstrictly hyperbolic systems with one space variable is studied in the case of jump discontinuities in the initial data. The same problem has been considered by \textit{L. Micheli} [Trans. Am. Math. Soc. 291, 451-485 (1985; Zbl 0597.35080)]. Here a simplified version is proposed, based on the regularity of the solutions of first order partial differential equations. Sharp estimates on the growth of some derivatives of the solution are obtained. They are used to prove a necessary and sufficient condition for the existence of anomalous singularities arising from the nonlinear interaction of singularities coming from the discontinuities of the initial data. In the corrigendum we supply counterexamples to results on the propagation of singularities of the solutions of one-dimensional semilinear weakly hyperbolic systems.