  We study the effect of directional quenching on patterns formed in simple
bistable systems such as the Allen-Cahn and the Cahn-Hilliard equation on the
plane. We model directional quenching as an externally triggered change in
system parameters, changing the system from monostable to bistable across an
interface. We are then interested in patterns forming in the bistable region,
in particular as the trigger progresses and increases the bistable region. We
find existence and non-existence results of single interfaces and striped
patterns.
