Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension

Details Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension

2010-10-04

arxiv.org/abs/1010.0618v1

Mathematics

Analysis of PDEs

57 pages

Scientific paper

We consider the semilinear wave equation with power nonlinearity in one space
dimension. We consider an arbitrary blow-up solution $u(x,t)$, the graph
$x\mapsto T(x)$ of its blow-up points and ${\cal S}\subset {\mathbb R}$ the set
of all characteristic points. We show that ${\ca S}$ is locally finite.

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