  Aims: We investigate the suitability of {\alpha}-viscosity in self-similar
models for self-gravitating disks with a focus on active galactic nuclei (AGN)
disks.
  Methods: We use a self-similar approach to simplify the partial differential
equations arising from the evolution equation, which are then solved using
numerical standard procedures.
  Results: We find a self-similar solution for the dynamical evolution of
self-gravitating {\alpha}-disks and derive the significant quantities. In the
Keplerian part of the disk our model is consistent with standard stationary
{\alpha}-disk theory, and self-consistent throughout the self-gravitating
regime. Positive accretion rates throughout the disk demand a high degree of
self-gravitation. Combined with the temporal decline of the accretion rate and
its low amount, the model prohibits the growth of large central masses.
  Conclusions: {\alpha}-viscosity cannot account for the evolution of the whole
mass spectrum of super-massive black holes (SMBH) in AGN. However, considering
the involved scales it seems suitable for modelling protoplanetary disks.
  Keywords: accretion, accretion disks, turbulence, hydrodynamics, methods:
analytical
