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

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 [4] 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.