The lifespan of solutions to wave equations with weighted nonlinear terms in one space dimension

TL;DR

This paper investigates the lifespan of solutions to one-dimensional nonlinear wave equations with weighted nonlinear terms, providing improved bounds that are shown to be optimal, advancing understanding of solution longevity.

Contribution

It introduces new upper and lower bounds for the lifespan of solutions, demonstrating their optimality, thus refining previous results on wave equations with weighted nonlinearities.

Findings

Improved upper bound for solution lifespan

Derived matching lower bound confirming optimality

Enhanced understanding of nonlinear wave equation behavior

Abstract

In this paper, we consider the initial value problem for nonlinear wave equation with weighted nonlinear terms in one space dimension. Kubo & Osaka & Yazici(2013) studied global solvability of the problem under different conditions on the nonlinearity and initial data, together with an upper bound of the lifespan for the problem. The aim of this paper is to improve the upper bound of the lifespan and to derive its lower bound which shows the optimality of our new upper bound.