The subject of this work are one-dimensional kinetic BGK models, regarded as relaxation models for genuinely non-linear scalar conservation laws. Kinetic profiles of shock waves in the form of travelling wave solutions of the kinetic model are studied. In particular, recent results on the existence and dynamic stability of small amplitude travelling waves are reviewed, and a new result on the existence of big travelling waves is proven.

Received: 2004-12-01
Revised :
Accepted: