Yuki Haruyama | Searcharxiv

arXiv2025

Note on the existence of classical solutions of derivative semilinear models for one dimensional wave equation

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.

math.AP↗

arXiv2024

Blow-up of classical solutions of quasilinear wave equations in one space dimension

This paper studies the upper bound of the lifespan of classical solutions of the initial value problems for one dimensional wave equations with quasilinear terms of space-, or time-derivatives of the unknown function. The results are same as those of the semilinear case. But it is quite meaningful to consider this kind of problems for the purpose to cover the optimality of the general theory for nonlinear wave equations by many model equations as far as possible.

math.AP↗