%0 Journal Article
%T Semilinear hyperbolic systems in one space dimension with strongly singular initial data
%A Kirsten E. Travers
%J Electronic Journal of Differential Equations
%D 1997
%I Texas State University
%X In this article interactions of singularities in semilinear hyperbolic partial differential equations in R^2 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.
%K anomalous singularities
%K semilinear hyperbolic equations
%K delta waves.
%U http://ejde.math.txstate.edu/Volumes/1997/14/abstr.html