Travers, Kirsten E.2018-11-052018-11-051997-08-28Travers, K. E. (1997). Semilinear hyperbolic systems in one space dimension with strongly singular initial data. <i>Electronic Journal of Differential Equations, 1997</i>(14), pp. 1-11.1072-6691https://hdl.handle.net/10877/7774In this article interactions of singularities in semilinear hyperbolic partial differential equations in ℝ2 are studied. Consider a simple non-linear system of three equations with derivatives of Dirac delta functions as initial data. As the micro-local linear theory prescribes, the initial singularities propagate along forward bicharacteristics. But there are also anomalous singularities created when these characteristics intersect. Their regularity satisfies 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.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalAnomalous singularitiesSemilinear hyperbolic equationsDelta wavesArticle