The behaviour of induced discontinuities behind a first order discontinuity wave for a quasi-linear hyperbolic system
type: Item
instance of: scholarly article
title: The behaviour of induced discontinuities behind a first order discontinuity wave for a quasi-linear hyperbolic system
zbMATH Open document ID: 0619.35072
DOI: 10.1007/BF00944921
author: A. Borrelli
author: M. C. Patria
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1987-01-01T00:00:00Z
review text: The authors study the propagation in a constant state of the induced discontinuities associated with a first order discontinuity wave for a quasi-linear hyperbolic system. Making use of the theory of singular surfaces and the ray-theory, we derive and solve completely the equations which the discontinuity vector \(\vec\omega\) must obey along the rays associated with the wave front. So we determine the evolution law of \(\vec\omega\) and find that it depends nonlinearly on the first order discontinuities and on the geometrical features of the wave front; thus the behaviour of the induced discontinuities is known once the evolution law of the first order discontinuity wave is obtained explicitly.
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4004764
zbMATH Keywords: propagation
zbMATH Keywords: induced discontinuities
zbMATH Keywords: quasi-linear hyperbolic system
zbMATH Keywords: singular surfaces
zbMATH Keywords: ray-theory
zbMATH Keywords: wave front
MaRDI profile type: Publication
cites work: Q3944964
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description: scientific article; zbMATH DE number 4004764