The behaviour of induced discontinuities behind a first order discontinuity wave for a quasi-linear hyperbolic system
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.
scientific article; zbMATH DE number 4004764
scientific article