Donninger, RolandSchörkhuber, Birgit2012-10-032012-10-032012-10-03201410.1090/S0002-9947-2013-06038-2https://infoscience.epfl.ch/handle/20.500.14299/85899We study the semilinear wave equation $\displaystyle \partial _t^2 \psi -\Delta \psi =\vert\psi \vert^{p-1}\psi $ for $ p > 3$ with radial data in three spatial dimensions. There exists an explicit solution which blows up at $ t=T>0$ given by $\displaystyle \psi ^T(t,x)=c_p (T-t)^{-\frac {2}{p-1}}, $ where $ c_p$ is a suitable constant. We prove that the blow up described by $ \psi ^T$ is stable in the sense that there exists an open set (in a topology strictly stronger than the energy) of radial initial data that leads to a solution which converges to $ \psi ^T$ as $ t\to T-$ in the backward lightcone of the blow up point $ (t,r)=(T,0)$.FOCUSING NONLINEARITYRADIAL SOLUTIONSUNIVERSALITYPROFILEtext::journal::journal article::research article