  We address the nature of the giant clumps in high-z galaxies that undergo
Violent Disc Instability, attempting to distinguish between long-lived clumps
that migrate inward and short-lived clumps that disrupt by feedback. We study
the evolution of clumps as they migrate through the disc using an analytic
model tested by simulations and confront theory with CANDELS observations. The
clump ``bathtub" model, which considers gas and stellar gain and loss, is
characterized by four parameters: the accretion efficiency, the
star-formation-rate (SFR) efficiency, and the outflow mass-loading factors for
gas and stars. The relevant timescales are all comparable to the migration
time, two-three orbital times. A clump differs from a galaxy by the internal
dependence of the accretion rate on the varying clump mass. The analytic
solution, involving exponential growing and decaying modes, reveals a main
evolution phase during the migration, where the SFR and gas mass are constant
and the stellar mass is rising linearly with time. This makes the inverse of
the specific SFR an observable proxy for clump age. Later, the masses and SFR
approach an exponential growth with a constant specific SFR, but this phase is
hypothetical as the clump disappears in the galaxy center. The model matches
simulations with different, moderate feedback, both in isolated and
cosmological settings. The observed clumps agree with our theoretical
predictions, indicating that the massive clumps are long-lived and migrating. A
non-trivial challenge is to model feedback that is non-disruptive in massive
clumps but suppresses SFR to match the galactic stellar-to-halo mass ratio.
