Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the intersection of sets of incoming and outgoing waves

Authors: Adi Ditkowski and Michael Sever
Journal: Quart. Appl. Math. 66 (2008), 1-26
MSC (2000): Primary 35Lxx, 35Qxx, 78Axx
DOI: https://doi.org/10.1090/S0033-569X-07-01080-3
Published electronically: January 10, 2008
MathSciNet review: 2396650
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Abstract: In the neighborhood of a boundary point, the solution of a first-order symmetric homogenous hyperbolic system is conveniently decomposed into fundamental waves solutions that are readily classified as outgoing, incoming, and stationary, or tangential.

Under a broad hypothesis, we show that the spans of the sets of outgoing and incoming waves have nontrivial intersection. Under these conditions, local, linear, perfectly nonreflecting local boundary conditions are shown to be an impossibility.

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Additional Information

Adi Ditkowski
Affiliation: School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

Michael Sever
Affiliation: Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel

DOI: https://doi.org/10.1090/S0033-569X-07-01080-3
Received by editor(s): February 17, 2006
Published electronically: January 10, 2008
Additional Notes: This research was supported by the Israel Science Foundation (grant No. 1364/04).
Article copyright: © Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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