Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation

Abstract

We consider the 1-dimensional semilinear wave equation with power nonlinearity. We consider an arbitrary blowup solution $u(x,t)$, the graph $x\mapsto T\left(x\right)$ of its blowup points, and $\mathcal{S}\subset \mathbb{R}$ the set of all characteristic points. We show that $\mathcal{S}$ is locally finite.