Criteria of the existence of global solutions to semilinear wave
equations with first-order derivatives on exterior domains
Criteria of the existence of global solutions to semilinear wave
equations with first-order derivatives on exterior domains
We study the existence of global solutions to semilinear wave equations on exterior domains $\mathbb{R}^n\setminus\mathcal{K}$, $n\geq2$, with small initial data and nonlinear terms $F(\partial u)$ where $F\in C^\kappa$ and $\partial^{\leq\kappa}F(0)=0$. If $n\geq2$ and $\kappa>n/2$, criteria of the existence of a global solution for general initial data are provided, except for …