Geodesic
Semilinear hyperbolic systems in one space dimension with strongly singular initial data
Electronic Journal of Differential Equations, Tome 1997 (1997).

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Summary: 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.
Classification : 35L455, 35L60
Keywords: anomalous singularities, semilinear hyperbolic equations, delta waves 
@article{EJDE_1997__1997__a42,
     author = {Travers, Kirsten E.},
     title = {Semilinear hyperbolic systems in one space dimension with strongly singular initial data},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1997},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a42/}
}
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Travers, Kirsten E. Semilinear hyperbolic systems in one space dimension with strongly singular initial data. Electronic Journal of Differential Equations, Tome 1997 (1997). http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a42/