  In this paper a strongly degenerate parabolic equation derived from a density
dependent particle flow model is studied. Furthermore, a free boundary problem
and its connection to the strongly degenerate parabolic equation is
investigated. First, it is shown that the strongly degenerate parabolic
equation has a unique global bounded weak solution that converges towards a
steady state for large time horizons. Two scenarios might occur: When the
average density $\rho_{\infty}$ is larger than a certain critical density
$\rho_{cr}$, the steady state coincides with $\rho_{\infty}$ and the
convergence rate is exponential in the $L^2$ norm; while in the opposite case
$\rho_{\infty}<\rho_{cr}$, the steady state is unknown and the convergence is
algebraic in a negative Sobolev seminorm. Further investigations show that for
radially symmetric and decreasing initial data, the solution of the strongly
degenerate parabolic equation can be constructed by using the solution of a
corresponding free boundary problem. Moreover, the global existence of weak
solutions to the latter problem is proved. Finally, numerical experiments in
two space dimensions are presented, which show that segregation phenomena can
appear when the initial average density is smaller than the critical density.
