Blow-up behavior outside the origin for a semilinear wave equation in the radial case

Details Blow-up behavior outside the origin for a semilinear wave equation in the radial case Blow-up behavior outside the origin for a semilinear wave equation in the radial case

2011-02-07

arxiv.org/abs/1102.1328v1

Mathematics

Analysis of PDEs

21 pages

Scientific paper

We consider the semilinear wave equation in the radial case with conformal subcritical power nonlinearity. If we consider a blow-up point different from the origin, then we exhibit a new Lyapunov functional which is a perturbation of the one dimensional case and extend all our previous results known in the one-dimensional case. In particular, we show that the blow-up set near non-zero non-characteristic points is of class $C^1$, and that the set of characteristic points is made of concentric spheres in finite number in $\{\frac 1R \le |x|\le R\}$ for any $R>1$.

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