Smooth solutions for a p-system of mixed elliptic-hyperbolic type

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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.

Original languageEnglish
Pages (from-to)189-198
Number of pages10
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Oct 2013

All Science Journal Classification (ASJC) codes

  • General Mathematics


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