On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations

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

References in corpus (3)

• Blow-up behavior for the Klein-Gordon and other perturbed semilinear wave equations
• Blow-up results for semilinear wave equations in the super-conformal case
• Smooth solutions to the nonlinear wave equation can blow up on Cantor sets

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