Evolution of Thin Discs with Partial Accretion

The viscous evolution of a thin disc around a central object is considered. Such discs are described by self-similar solutions in which either all or none of the inflowing mass accretes. An approximate solution for the partial accretion regime is constructed by employing a prescription recently introduced for nonlinear heat conduction. The solution is compared with numerical simulations demonstrating that the approximate solution describes the intermediate asymptotic stage for partially accreting discs.