## Stable self-similar blow up for energy subcritical wave equations    [PDF]

Roland Donninger, Birgit Schörkhuber
We consider the semilinear wave equation $\partial_t^2 \psi-\Delta \psi=|\psi|^{p-1}\psi$ for $1equation admits an explicit spatially homogeneous blow up solution$\psi^T$given by $$\psi^T(t,x)=\kappa_p (T-t)^{-\frac{2}{p-1}}$$ where$T>0$and$\kappa_p$is a$p$-dependent constant. We prove that the blow up described by$\psi^T\$ is stable against small perturbations in the energy topology. This
complements previous results by Merle and Zaag. The method of proof is quite
robust and can be applied to other self-similar blow up problems as well, even
in the energy supercritical case.
View original: http://arxiv.org/abs/1201.4337