  New model equations are derived for dynamics of self-aggregation of
finite-size particles. Differences from standard Debye-Huckel and Keller-Segel
models are: a) the mobility $\mu$ of particles depends on the locally-averaged
particle density and b) linear diffusion acts on that locally-averaged particle
density. The cases both with and without diffusion are considered here.
Surprisingly, these simple modifications of standard models allow progress in
the analytical description of evolution as well as the complete analysis of
stationary states. When $\mu$ remains positive, the evolution of collapsed
states in our model reduces exactly to finite-dimensional dynamics of
interacting particle clumps. Simulations show these collapsed (clumped) states
emerging from smooth initial conditions, even in one spatial dimension. If
$\mu$ vanishes for some averaged density, the evolution leads to spontaneous
formation of \emph{jammed patches} (weak solution with density having compact
support). Simulations confirm that a combination of these patches forms the
final state for the system.
