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

Abstract

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 $\mathcal{S}\subset \mathbb{R}$ the set of all characteristic points. We show that ${\ca S}$ is locally finite.

arXiv comment57 pages

References in corpus (2)

• Smooth solutions to the nonlinear wave equation can blow up on Cantor sets
• Construction of a multi-soliton blow-up solution to the semilinear wave equation in one space dimension

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