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The exceptional condition and unboundedness of solutions of hyperbolic systems of conservation type

Published online by Cambridge University Press:  14 February 2012

A. Jeffrey
A. Jeffrey
Affiliation:
Department of Engineering Mathematics, University of Newcastle upon Tyne
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Synopsis

This paper is concerned with quasilinear hyperbolic systems of conservation type and establishes two main results. The first is that when a general system is considered in one space dimension and time, then the exceptional nature of a characteristic field implies the coincidence of a shock with one of the characteristics of that field. The second result involves the demonstration by example that quasilinear hyperbolic systems of conservation type may possess solutions that become unbounded after only a finite time, even though they are exceptional.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 1-2 , 1977 , pp. 1 - 8
Copyright
Copyright © Royal Society of Edinburgh 1977

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