We find the Green ’ s functions for the accretion disk with the fixed outer radius and time-independent viscosity .
With the Green ’ s functions , a viscous evolution of the disk with any initial conditions can be described .
Two types of the inner boundary conditions are considered : the zero stress tensor and the zero accretion rate .
The variable mass inflow at the outer radius can also be included .
The well-known exponential decline of the accretion rate is a part of the solution with the inner zero stress tensor .
The solution with the zero central accretion rate is applicable to the disks around stars with the magnetosphere ’ s boundary exceeding the corotation radius .
Using the solution , the viscous evolution of disks in some binary systems can be studied .
We apply the solution with zero inner stress tensor to outbursts of short-period X-ray transients during the time around the peak .
It is found that for the Kramers ’ regime of opacity and the initial surface density proportional to the radius , the rise time to the peak is t _ { \mathrm { rise } } \approx 0.15 r _ { \mathrm { out } } ^ { 2 } / \nu _ { \mathrm { out } } and the e -folding time of the decay is t _ { \mathrm { exp } } \approx 0.45 r _ { \mathrm { out } } ^ { 2 } / \nu _ { \mathrm { out } } .
Comparison to non-stationary \alpha -disks shows that both models with the same value of viscosity at the outer radius produce similar behaviour on the viscous time-scale .
For six bursts in X-ray novae , which exhibit fast-rise-exponential-decay and are fitted by the model , we find a way to restrict the turbulent parameter \alpha .