TY - JOUR
T1 - Smooth solutions for a p-system of mixed elliptic-hyperbolic type
AU - Bialy, Misha
N1 - Funding Information:
∗ Partially supported by ISF grant 128/10. Received April 30, 2012
PY - 2013/10
Y1 - 2013/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84883813131&partnerID=8YFLogxK
U2 - 10.1007/s11856-012-0183-0
DO - 10.1007/s11856-012-0183-0
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AN - SCOPUS:84883813131
SN - 0021-2172
VL - 197
SP - 189
EP - 198
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -