The behaviour of induced discontinuities behind a first order discontinuity wave for a quasi-linear hyperbolic system

  • Alessandra Borrelli
  • Maria Cristina Patria
Original Papers

Summary

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\(\mathop \omega \limits^*\) must obey along the rays associated with the wave front. So we determine the evolution law of\(\mathop \omega \limits^*\) 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.

Keywords

Mathematical Method Wave Front Geometrical Feature Hyperbolic System Constant State 

Riassunto

In questa nota studiamo la propagazione, in uno stato costante, delle discontinuità indotte associate a un'onda di discontinuità del primo ordine per un sistema iperbolico quasi-lineare. Adottando un'opportuna combinazione della teoria delle superfici singolari e delle teoria dei raggi, determiniamo in maniera completa il comportamento del vettore delle discontinuità indotte\(\mathop \omega \limits^*\) lungo i raggi associati al fronte d'onda. Troviamo che la legge di evoluzione di\(\mathop \omega \limits^*\) dipende non linearmente dalle discontinuità del primo ordine e dalle caratteristiche geometriche del fronte d'onda. L'andamento di\(\mathop \omega \limits^*\) è perciò noto una volta nota esplicitamente la legge di evoluzione delle discontinuità del primo ordine.

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Copyright information

© Birkhäuser Verlag 1987

Authors and Affiliations

  • Alessandra Borrelli
    • 1
  • Maria Cristina Patria
    • 1
  1. 1.Dipartimento di MatematicaUniversitá di FerraraFerraraItaly

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