Travers, Kirsten E. Semilinear hyperbolic systems in one space dimension with strongly singular initial data. (English) Zbl 0886.35090 Electron. J. Differ. Equ. 1997, Paper 14, 11 p. (1997). Summary: Interactions of singularities in semilinear hyperbolic partial differential equations in \(\mathbb{R}^2\) are studied. Consider a simple nonlinear system of three equations with derivatives of Dirac delta functions as initial data. As the microlocal 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. Cited in 2 Documents MSC: 35L45 Initial value problems for first-order hyperbolic systems 35L60 First-order nonlinear hyperbolic equations 35A20 Analyticity in context of PDEs Keywords:anomalous singularities; derivatives of Dirac delta functions as initial data PDFBibTeX XMLCite \textit{K. E. Travers}, Electron. J. Differ. Equ. 1997, Paper 14, 11 p. (1997; Zbl 0886.35090) Full Text: EuDML EMIS