The lifespan estimates of classical solutions of one dimensional semilinear wave equations with characteristic weights

TL;DR

This paper investigates the lifespan of classical solutions to one-dimensional semilinear wave equations with characteristic weights, focusing on time-variable weights and their interactions in characteristic directions.

Contribution

It provides new lifespan estimates for solutions with characteristic weights, especially for time-variable weights, expanding understanding of wave equation behavior.

Findings

Lifespan estimates for solutions with time-variable weights.

Analysis of interactions between two characteristic directions.

Exclusion of certain space-variable weight cases.

Abstract

In this paper, we study the lifespan estimates of classical solutions for semilinear wave equations with characteristic weights and compactly supported data in one space dimension. The results include those for weights by time-variable, but exclude those for weights by space-variable in some cases. We have interactions of two characteristic directions.