The lifespan of classical solutions to nonlinear wave equations in two space dimensions (Q1207185)

The authors study the lifespan of solutions to the initial value problems for nonlinear wave equations of the form \[ \partial_ t^ 2 u(x,t)- \Delta u(x,t)=A| u(x,t)|^ p, \] \[ u(x,0)=f(x),\;\partial_ t u(x,0)=g(x), \quad x\in\mathbb{R}^ n, \quad (x,t)\in\mathbb{R}^ n\times [0,\infty), \] where \(p\) and \(A\) are positive constants and \(n=2,3\). The main aim of this paper is to look for the upper and lower bounds for the lifespan in two space dimensions.