Semilinear hyperbolic systems in one space dimension with strongly singular initial data

Abstract. In this article interactions of singularities in semilinear hyperbolic partial dierential equations are studied. Consider a simple non-linear system of three equations in R2 with derivatives of Dirac delta functions as initial data. As the micro-local linear theory prescribes, the initial singularities propagate along forward bicharacteristics. However, there are also anomalous singulari-ties created when these characteristics intersect. Their regularity satises the following \sum law": the \strength " of the anomalous singularity equals the sum of the \strengths " of the incoming singularities. Hence the solution to the system becomes more singular as time progresses. 1