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

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 {1/R <= vertical bar x vertical bar <= R} for any R > 1. (C) 2011 Elsevier Masson SAS. All rights reserved.