In the present paper we study the propagation into 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 induced discontinuity vector {Mathematical expression} must obey along the rays associated with the wave front. So we determine the evolution law of {Mathematical expression} and find that it depends non-linearly 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. © 1987 Birkhäuser Verlag.
The behaviour of induced discontinuities behind a first order discontinuity wave for a quasilinear hyperbolic system
BORRELLI, Alessandra;PATRIA, Maria Cristina
1987
Abstract
In the present paper we study the propagation into 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 induced discontinuity vector {Mathematical expression} must obey along the rays associated with the wave front. So we determine the evolution law of {Mathematical expression} and find that it depends non-linearly 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. © 1987 Birkhäuser Verlag.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
