Forced Frequency Locking for Semilinear Dissipative Hyperbolic PDEs
Analysis of PDEs
2025-12-10 v1
Abstract
This paper concerns the behavior of time-periodic solutions to 1D dissipative autonomous semilinear hyperbolic PDEs under the influence of small time-periodic forcing. We show that the phenomenon of forced frequency locking happens similarly to the analogous phenomena known for ODEs or parabolic PDEs. However, the proofs are essentially more difficult than for ODEs or parabolic PDEs. In particular, non-resonance conditions are needed, which do not have counterparts in the cases of ODEs or parabolic PDEs. We derive a scalar equation which answers the main question of forced frequency locking: Which time shifts of the solution to the unforced equation do survive under which forcing?
Cite
@article{arxiv.2208.00868,
title = {Forced Frequency Locking for Semilinear Dissipative Hyperbolic PDEs},
author = {Irina Kmit and Lutz Recke},
journal= {arXiv preprint arXiv:2208.00868},
year = {2025}
}
Comments
47 pages