  It is generally believed that gaseous disks around supermassive black hole
(SMBH) binaries in centers of galaxies can facilitate binary merger and give
rise to observational signatures both in electromagnetic and gravitational wave
domains. We explore general properties of circumbinary disks by reformulating
standard equations for the viscous disk evolution in terms of the viscous
angular momentum flux F_J. In steady state F_J is a linear function of the
specific angular momentum, which is a generalization of (but is not equivalent
to) the standard constant \dot M disk solution. If the torque produced by the
central binary is effective at stopping gas inflow and opening a gap (or
cavity) in the disk, then the inner part of the circumbinary disk can be
approximated as a constant F_J disk. We compute properties of such disks in
different physical regimes relevant for SMBH binaries and use these results to
understand the gas-assisted evolution of SMBH pairs starting at separations
10^{-4}-10^{-2} pc. We find the following. (1) Pile-up of matter at the inner
edge of the disk leads to continuous growth of the torque acting on the binary
and can considerably accelerate its orbital evolution compared to the
gravitational wave-driven decay. (2) Torque on the binary is determined
non-locally and does not in general reflect the disk properties in the vicinity
of the binary. (3) Binary evolution depends on the past history of the disk
evolution. (4) Eddington limit can be important in circumbinary disks even if
they accrete at sub-Eddington rates at late stages of binary evolution. (5)
Circumbinary disk self-consistently evolved under the action of the binary
torque emits more power and has spectrum different from the spectrum of
constant \dot M disk - it is steeper (\nu F_\nu\propto \nu^{12/7}) and extends
to shorter wavelength, facilitating its detection.
