Improvement of the general theory for one dimensional nonlinear wave equations related to the combined effect

2023/08/04 by Shu Takamatsu, Takamatsu, Shu · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #primary 35L70 #secondary 35A01

paper · pdf · doi:10.48550/arxiv.2308.02174

openalex publication_date 2023/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We focus on the general theory to the Cauchy problem for one dimensional nonlinear wave equations with small initial data. In the general theory, we aim to obtain the lower bound estimate of the lifespan of classical solution. In this paper, we improve it in some case related to the combined effect, which was expected complete more than 30 years ago.

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