# zbMATH — the first resource for mathematics

Hyperbolicity for systems. (English) Zbl 1061.35046
Begehr, Heinrich G. W. (ed.) et al., Analysis and applications–ISAAC 2001.
Proceedings of the 3rd international congress, Berlin, Germany, August 20–25, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1384-1/hbk). Int. Soc. Anal. Appl. Comput. 10, 237-252 (2003).
The author investigates for which systems of linear partial differential operators the Cauchy problem is $$C^\infty$$ well posed for any lower order terms (strong hyperbolicity), or for which systems the Cauchy problem is $$C^\infty$$ well posed (hyperbolicity). In this paper he presents a survey of the subject, in particular focussing the interests on the necessary conditions for strong hyperbolicity or just hyperbolicity.
For the entire collection see [Zbl 1031.35002].

##### MSC:
 35L30 Initial value problems for higher-order hyperbolic equations
##### Keywords:
strong hyperbolicity; $$C^\infty$$ well posedness