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

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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