  We analyse a DGP brane filled with a k-essence field and assume the k-field
evolving linearly with the cosmic time of the brane. We then solve analytically
the Friedmann equation and deduce the different behaviour of the brane at the
low and the high energy regimes. The asymptotic behaviour can be quite
different involving accelerating branes, big bangs, big crunches, big rips or
quiescent singularities. The latter correspond to a type of sudden singularity.
