  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 $R>1$.
