  We consider an explicit self-similar solution to an energy-supercritical
Yang-Mills equation and prove its mode stability. Based on earlier work by one
of the authors, we obtain a fully rigorous proof of the nonlinear stability of
the self-similar blowup profile. This is a large-data result for a
supercritical wave equation. Our method is broadly applicable and provides a
general approach to stability problems related to self-similar solutions of
nonlinear wave equations.
