Smooth solutions for a p-system of mixed elliptic-hyperbolic type |
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Authors: | Misha Bialy |
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Institution: | 1. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel
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Abstract: | 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. |
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