The lifespan of classical solutions of semilinear wave equations with spatial weights and compactly supported data in one space dimension

TL;DR

This paper investigates the lifespan of classical solutions to semilinear wave equations with spatial weights in one dimension, providing lifespan estimates based on initial data and weight types, classified by initial speed integral.

Contribution

It offers new lifespan estimates for semilinear wave equations with polynomial weights, considering the impact of initial speed integral in one-dimensional space.

Findings

Lifespan estimates are established for all polynomial weight cases.

Solutions' lifespan depends on the total initial speed integral.

Classification into two cases based on initial data integral.

Abstract

This paper studies initial value problems for semilinear wave equations with spatial weights in one space dimension. The lifespan estimates of classical solutions for compactly supported data are established in all the cases of polynomial weights. The results are classified into two cases according to the total integral of the initial speed.