Response solutions for wave equations with variable wave speed and periodic forcing
Dynamical Systems
2020-07-03 v2
Abstract
We consider a model of nonlinear wave equations with periodically varying wave speed and periodic external forcing. By imposing non-resonance conditions on the frequency, we establish the existence of the response solutions (i.e., periodic solutions with the same frequency as the forcing) for such a model in a Cantor set of asymptotically full measure. The proof relies on a Lyapunov--Schmidt reduction together with the Nash--Moser iteration.
Cite
@article{arxiv.1711.09437,
title = {Response solutions for wave equations with variable wave speed and periodic forcing},
author = {Bochao Chen and Yixian Gao and Yong Li and Xue Yang},
journal= {arXiv preprint arXiv:1711.09437},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1706.03921