  By means of a simple model we investigate the possibility of an accelerated
expansion of a 3-dimensional subspace in the presence of the variation of the
effective 4-dimensional constant obeying the experimental constraint.
Multidimensional cosmological solutions with m 2-form fields and l scalar
fields are presented. Solutions corresponding to rank-3 Lie algebras are
singled out and discussed. Each of solutions contain two factor spaces:
one-dimensional space M_1 and Ricci-flat space M_2. A 3-dimensional subspace of
M_2 is interpreted as "our" space. We show that there exists a time interval
where accelerated expansion of our 3D space is compatible with a small enough
variation of the effective gravitational constant G(\tau). This interval
contains \tau_0 which is the point of minimum of G(\tau) (here \tau is the
synchronous time variable). Special solutions with three phantom scalar fields
are analyzed. It is shown that in the vicinity of the point \tau_0 the time
variation of G(\tau) decreases in the sequence of Lie algebras A_3, C_3 and B_3
when the solutions with asymptotically power-law behavior of scale-factors for
\tau \to \infty are considered. Exact solutions with asymptotically exponential
accelerated expansion of 3D space are also considered.
