1201.4337 (Roland Donninger et al.)

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