Electronic Journal of Differential Equations,
Vol. 1997(1997), No. 14, pp 1-11.

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

Author: Kirsten E. Travers (Duke Univ.,  Durham, USA)

Abstract: 
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.

Submitted  March 24, 1997. Published August 28, 1997.
Math Subject Classification: 35L455, 35L60
Key Words: anomalous singularities; semilinear hyperbolic equations; 
           delta waves.