Life-span of classical solutions to one dimensional initial–boundary value problems for general quasilinear wave equations

Abstract

This paper is devoted to studying the initial–boundary value problem for one dimensional general quasilinear wave equations u t t − u x x = b ( u , D u ) u x x + 2 a 0 ( u , D u ) u t x + F ( u , D u ) on exterior domain. We obtain the sharp lower bound of the life-span of classical solutions to the initial–boundary value problem with small initial data and zero boundary data for one dimensional general quasilinear wave equations.