Note on the existence of classical solutions of derivative semilinear models for one dimensional wave equation
Abstract
This note is a supplement with a new result to the review paper by Takamura [13] on nonlinear wave equations in one space dimension. We are focusing here to the long-time existence of classical solutions of semilinear wave equations in one space dimension, especially with derivative nonlinear terms of product-type. Our result is an extension of the single component case, but it is meaningful to provide models as possible as many to cover the optimality of the general theory. The proof is based on the classical iteration argument of the point-wise estimate of the solution.
Keywords
Cite
@article{arxiv.2409.06378,
title = {Note on the existence of classical solutions of derivative semilinear models for one dimensional wave equation},
author = {Yuki Haruyama and Takiko Sasaki and Hiroyuki Takamura},
journal= {arXiv preprint arXiv:2409.06378},
year = {2025}
}
Comments
10 pages. The assumption of Theorem 4.1 is extended and Remark 4.3 as well as the reference [14] is added. This is the accepted version for Proceedings of the conference "Critical Phenomena in Nonlinear Partial Differential Equations, Harmonic Analysis, and Functional Inequalities."