Abstract:This paper deals with some examples of physically meaningfull models where the use of Genralized Functions allows to solve some situations where the usual ways are not always suitable since a product of non regular functions may occur. We first describe the modelization of very simple cases as the model of the velocity field corresponding to a temporary stop and restart (in road traffic, in biology for chrysalis,..). Then we show how to build an acceptable shock condition, even when the model is not a conservative one, for an application in elastodynamics, then in a general class of non homogeneous hyperbolic systems , including the Saint-Venant equations and many of the usual models occuring in Hydrodynamics, Wave equations, ... Next we present some interesting behaviours of solutions which can be profiled as the succession of many short shock waves and regular waves, as in the Roll waves phenomenon, approximating a regular curve which never corresponds to a solution by itself, but may be an example of a non trivial generalized solution.

**Paper:**- Available as PostScript (116 Kbytes) or gzipped PostScript (46 Kbytes; uncompress using gunzip).
**Author(s):**- Alain-Yves Le Roux, <AY.leroux@u-bordeaux.fr>
**Publishing information:****Comments:****Submitted by:**- <AY.leroux@u-bordeaux.fr> January 25 2002.

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