  We discuss a thin film evolution equation for a wetting evaporating liquid on
a smooth solid substrate. The model is valid for slowly evaporating small
sessile droplets when thermal effects are insignificant, while wettability and
capillarity play a major role. The model is first employed to study steady
evaporating drops that are fed locally through the substrate. An asymptotic
analysis focuses on the precursor film and the transition region towards the
bulk drop and a numerical continuation of steady drops determines their fully
non-linear profiles.
  Following this, we study the time evolution of freely evaporating drops
without influx for several initial drop shapes. As a result we find that drops
initially spread if their initial contact angle is larger than the apparent
contact angle of large steady evaporating drops with influx. Otherwise they
recede right from the beginning.
