  We consider the formation of finite-time quenching singularities for
solutions of semi-linear wave equations with negative power nonlinearities, as
can model micro-electro-mechanical systems (MEMS). For radial initial data we
obtain, formally, the existence of a sequence of quenching self-similar
solutions. Also from formal asymptotic analysis, a solution to the PDE which is
radially symmetric and increases strictly monotonically with distance from the
origin quenches at the origin like an explicit spatially independent solution.
The latter analysis and numerical experiments suggest a detailed conjecture for
the singular behaviour.
