On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations
arXiv:1309.7760 · doi:10.1007/s00220-014-2132-8
Abstract
We consider a blow-up solution for the semilinear wave equation in $N$ dimensions, with subconformal power nonlinearity. Introducing $\RR_0$ the set of non-characteristic points with the Lorentz transform of the space-independent solution as asymptotic profile, we show that $\RR_0$ is open and that the blow-up surface is of class $C^1$ on $\RR_0$. Then, we show the stability of $\RR_0$ with respect to initial data.
33 pages