Semilinear Hyperbolic Systems in one Space Dimension with Strongly Singular Initial Data

Date

1997-08-28

Authors

Travers, Kirsten E.

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

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.

Description

Keywords

Anomalous singularities, Semilinear hyperbolic equations, Delta waves

Citation

Travers, K. E. (1997). Semilinear hyperbolic systems in one space dimension with strongly singular initial data. <i>Electronic Journal of Differential Equations, 1997</i>(14), pp. 1-11.

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Attribution 4.0 International

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