  Planet migration originally refers to protoplanetary disks, which are more
massive and dense than typical accretion disks in binary systems. We study
planet migration in an accretion disk in a binary system consisting of a
solar-like star hosting a planet and a red giant donor star. The accretion disk
is fed by a stellar wind. %, disk self-gravity is neglected. We use the
$\alpha$-disk model and consider that the stellar wind is time-dependent.
Assuming the disk is quasi-stationary we calculate its temperature and surface
density profiles. In addition to the standard disk model, when matter is
captured by the disk at its outer edge, we study the situation when the stellar
wind delivers matter on the whole disc surface inside the accretion radius with
the rate depending on distance from the central star. Implying that a planet
experiences classical type I/II migration we calculate migration time for a
planet on a circular orbit coplanar with the disk. Potentially, rapid inward
planet migration can result in a planet-star merger which can be accompanied by
an optical or/and UV/X-ray transient. We calculate timescale of migration for
different parameters of planets and binaries. Our results demonstrate that
planets can fall on their host stars within the lifetime of the late-type donor
for realistic sets of parameters.
