Analyticity, Gevrey regularity and unique continuation for an integrable multi-component peakon system with an arbitrary polynomial function
Exactly Solvable and Integrable Systems
2015-11-12 v1 Analysis of PDEs
Abstract
In this paper, we study the Cauchy problem for an integrable multi-component (2N-component) peakon system which is involved in an arbitrary polynomial function. Based on a generalized Ovsyannikov type theorem, we first prove the existence and uniqueness of solutions for the system in the Gevrey-Sobolev spaces with the lower bound of the lifespan. Then we show the continuity of the data-to-solution map for the system. Furthermore, by introducing a family of continuous diffeomorphisms of a line and utilizing the fine structure of the system, we demonstrate the system exhibits unique continuation.
Cite
@article{arxiv.1511.03315,
title = {Analyticity, Gevrey regularity and unique continuation for an integrable multi-component peakon system with an arbitrary polynomial function},
author = {Qiaoyi Hu and Zhijun Qiao},
journal= {arXiv preprint arXiv:1511.03315},
year = {2015}
}