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15.—The Propagation of Second-order Lipschitz Discontinuities in Quasi-linear Hyperbolic Systems with Discontinuous Coefficients

Published online by Cambridge University Press:  14 February 2012

Alan Jeffrey  and
Esin Inan
Alan Jeffrey
Affiliation:
Department of Engineering Mathematics, University of Newcastle upon Tyne.
Esin Inan
Affiliation:
Department of Engineering Mathematics, University of Newcastle upon Tyne.
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Synopsis

This paper develops the general theory of the propagation of Lipschitz discontinuities in first- and second-order partial derivatives of the initial data for a conservative quasi-linear hyperbolic system with discontinuous coefficients. After establishing that such weak discontinuities propagate along characteristics the appropriate transport equations are derived. The effect on this form of wave propagation of the strong discontinuity associatedwith the discontinuous coefficients is then studied and the transmission and reflection characteristics of the resulting waves are analysed. In conclusion, an application of this general theory is made to the propagation of plane shear waves through two different continuous hyperelastic solids to determine the transmitted and reflected waves.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 74 , 1976 , pp. 205 - 224
Copyright
Copyright © Royal Society of Edinburgh 1976

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