ASYMPTOTIC BEHAVIOR OF NEUTRON TRANSPORT IN A SLAB WITH MOVING BOUNDARIES.

The problem under consideration includes a possible external source q(t,x, mu ) which converges to some q//0(x, mu ) as t approaches infinity . It is shown under certain conditions on the various cross-sections and the behavior of the moving boundary that a global solution to the time-dependent system exists and converges to a unique steady-state solution of the corresponding boundary-value problem. In particular, this solution converges to zero when q//0 equals 0. On the other hand, under a different condition on the same set of physical parameters the solution grows unbounded as t approaches infinity . These results lead to the stability and instability of the neutron transport in a multiplying transport medium. Explicit bounds for the time-dependent solution on any finite time interval are also given.