Electron. J. Diff. Eqns.,
Vol. 1997(1997), No. 14, pp 1-11.

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

Kirsten E. Travers

**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.

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Kirsten E. Travers

Department of Mathematics, Duke University,
Durham, NC 27708. USA

e-mail: kirsten@math.duke.edu,
web page

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