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

2014/09/20 by Kyouhei Wakasa, Wakasa, Kyouhei
Mathematics · #35A09 #35B44 #35E15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35L71 #Secondary 35A01 #math.AP #msc:35A01 #msc:35A09 #msc:35B44 #msc:35E15 #msc:35L71

paper · pdf · doi:10.48550/arxiv.1409.5877

17 pages

arxiv created 2014/09/20 · arxiv updated 2014/09/23

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.

Related

• Recent developments on the lifespan estimate for classical solutions of nonlinear wave equations in one space dimension
• The lifespan of solutions of semilinear wave equation with weighted nonlinearity
• Semilinear wave equations of derivative type with characteristic weights in one space dimension
• The sharp lower bound of the lifespan of solutions to semilinear wave equations with low powers in two space dimensions
• Lower Bound of the Lifespan of the Solution to Systems of Quasi-linear Wave Equations with Multiple Propagation Speeds