Smooth solutions for a ${p}$-system of mixed type
Analysis of PDEs
2012-04-20 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
In this note we analyze smooth solutions of a -system of the \textit{mixed} type. Motivating example for this is a 2-components reduction of the Benney moments chain which appears to be connected to theory of integrable systems. We don't assume a-priory 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 are necessarily constants. As for initial value problem we prove that if the initial data is strictly hyperbolic and periodic in then the solution can not extend to and shocks are necessarily created.
Cite
@article{arxiv.1204.4397,
title = {Smooth solutions for a ${p}$-system of mixed type},
author = {Michael and Bialy},
journal= {arXiv preprint arXiv:1204.4397},
year = {2012}
}