  We study the effect of a Jovian planet on the gas distribution of a
protoplanetary disc, using a new numerical scheme that allows us to take into
consideration the global evolution of the disc, down to an arbitrarily small
inner physical radius. We find that Jovian planets do not open cavities in the
inner part of the disc (i.e. interior to their orbits) unless (a) the inner
physical edge of the disc is close to the planet's location or (b) the planet
is much more massive than the disc. In all other cases the planet simply opens
a gap in the gas density distribution, whose global profile is essentially
unchanged relative to the one that it would have if the planet were absent. We
recognize, though, that the dust distribution can be significantly different
from the gas distribution and that dust cavities might be opened in some
situations, even if the gas is still present in the inner part of the disc.
  Concerning the migration of the planet, we find that classical Type-II
migration (with speed proportional to the viscosity of the disc) occurs only if
the gap opened by the planet is deep and clean. If there is still a significant
amount of gas in the gap, the migration of the planet is generally slower than
the theoretical Type-II migration rate. In some situations, migration can be
stopped or even reversed. We develop a simple model that reproduces
satisfactorily the migration rate observed in the simulations, for a wide range
of disc viscosities and planet masses and locations relative to the inner disc
edge. Our results are relevant for extra-solar planetary systems, as they
explain (a) why some hot Jupiters did not migrate all the way down to their
parent stars and (b) why the outermost of a pair of resonant planets is
typically the most massive one.
