Semilinear Hyperbolic Systems in one Space Dimension with Strongly Singular Initial Data
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In this article interactions of singularities in semilinear hyperbolic partial differential equations in ℝ2 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.
CitationTravers, K. E. (1997). Semilinear hyperbolic systems in one space dimension with strongly singular initial data. Electronic Journal of Differential Equations, 1997(14), pp. 1-11.
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