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arXiv · 1309.7760

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

Frank Merle·Hatem Zaag
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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.

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Frank Merle, Hatem Zaag. 2014-03-09. On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. https://doi.org/10.1007/s00220-014-2132-8

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