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.