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

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dc.contributor.authorTravers, Kirsten E.
dc.date.accessioned2018-11-05T14:53:38Z
dc.date.available2018-11-05T14:53:38Z
dc.date.issued1997-08-28
dc.description.abstractIn 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent11 pages
dc.format.medium1 file (.pdf)
dc.identifier.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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/7774
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 1997, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectAnomalous singularities
dc.subjectSemilinear hyperbolic equations
dc.subjectDelta waves
dc.titleSemilinear Hyperbolic Systems in one Space Dimension with Strongly Singular Initial Dataen_US
dc.typeArticle

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