  We consider an initial value problem for a nonlocal differential equation
with a bistable nonlinearity in several space dimensions. The equation is an
ordinary differential equation with respect to the time variable t, while the
nonlocal term is expressed in terms of spatial integration. We discuss the
large time behavior of solutions and prove, among other things, the convergence
to steady-states. The proof that the solution orbits are relatively compact is
based upon the rearrangement theory.
