  We explain the force balance in flowing marine ice sheets and the ice shelves
they often feed. Treating ice as a viscous shear-thinning power law fluid, we
develop an asymptotic (late-time) theory in two cases $-$ the presence or
absence of contact with sidewalls. The solution without sidewalls is a simple
generalisation of that found by Robison (JFM, 648, 363), allowing us to obtain
the equilibrium grounding line thickness using a simple computer model and to
get an analytic approximation. For laterally confined shelves, we obtain an
asymptotic theory valid for long shelves and define when this is. Our theory is
based on the velocity profile across the channel being a generalised version of
Poiseuille flow, which works when lateral shear dominates the force balance.
  We conducted experiments using a laboratory model for ice. This was an
aqueous suspension of $0.5\%$ mass concentration xanthan, yielding $n \approx
3.8$ (similar to ice). Our theories agreed extremely well with our experiments
for all relevant parameters (front position, thickness profile, lateral
velocity profile, longitudinal velocity gradient and grounding line thickness).
This strongly suggests that we have understood the dominant force balance in
both types of ice shelf.
  In the real world, ice tongues are unlikely to rapidly disintegrate but can
be shortened until they no longer exist, at which point the sheet becomes
unstable and ultimately the grounding line should retreat above sea level.
Prior to that point, the flow of ice into it should not be speeded up and the
grounding line should also not retreat, assuming that only oceanic conditions
change. However, laterally confined ice shelves experience significant
buttressing. If removed, this leads to a rapid speedup of the sheet and a much
smaller equilibrium grounding line thickness. Something similar may have
occurred to the Larsen B ice shelf.
