naa a22 4500 510783570 CHVBK 20180411083255.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s11856-012-0183-0 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0183-0 Bialy Misha School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel aut Smooth solutions for a p -system of mixed elliptic-hyperbolic type [Elektronische Daten] [Misha Bialy] In this note we analyze smooth solutions of a p-system of the mixed, elliptic-hyperbolic type. A motivating example for this is a 2-components reduction of the Benney moments chain which appears to be connected to the theory of integrable systems. We don't assume a-priori that the solutions in question are in the Hyperbolic region. Our main result states that the only smooth solutions of the system which are periodic in x are necessarily constants. As for the initial value problem, we prove that if the initial data are strictly hyperbolic and periodic in x, then the solution cannot extend to [t 0;+∞) and shocks are necessarily created. Hebrew University Magnes Press, 2013 Israel Journal of Mathematics Springer US; http://www.springer-ny.com 197/1(2013-10-01), 189-198 0021-2172 197:1<189 2013 197 11856 https://doi.org/10.1007/s11856-012-0183-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0183-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bialy Misha School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 197/1(2013-10-01), 189-198 0021-2172 197:1<189 2013 197 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer