The Kawahara equation on star graphs
Analysis of PDEs
2025-11-18 v2
Abstract
In this paper, we establish local well-posedness for the Cauchy problem associated with the Kawahara equation on a general metric star graph. Initially, we identify suitable boundary conditions that produce a well-behaved dynamics for the linear equation. Subsequently, we derive the integral formula using the forcing operator method, previously applied to the Kawahara equation on the half-line by Cavalcante and Kwak (NoDEA 2020), and the Fourier restriction method of Bourgain (GAFA 1993). This work has the potential to be extended to other fifth-order nonlinear dispersive equations on star graphs.
Cite
@article{arxiv.2511.06007,
title = {The Kawahara equation on star graphs},
author = {Márcio Cavalcante and Chulkwang Kwak and José Marques},
journal= {arXiv preprint arXiv:2511.06007},
year = {2025}
}
Comments
References that appear in the abstract have been corrected. Comments are welcome