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.
Rights
Attribution 4.0 International