  We study closed dense collections of hard spheres that collide inelastically
with constant coefficient of normal restitution. We find inhomogeneous states
(IS) where the density profile is spatially non-uniform but constant in time.
The states are exact solutions of non-linear partial differential equations
that describe the coupled distributions of density and temperature when
inelastic losses of energy per collision are small. The derivation is performed
without modelling the equations' coefficients that are unknown in the dense
limit (such as the equation of state), using only their scaling form specific
for hard spheres. The IS is exact non-linear state of this many-body system. It
captures a fundamental property of inelastic collections of particles: the
possibility of preserving non-uniform temperature via the interplay of
inelastic cooling and heat conduction, generalizing previous results in the
dilute case. We perform numerical simulations to demonstrate that arbitrary
initial state evolves to the IS in the limit of long times where the container
has the geometry of the channel. The evolution is like gas-liquid transition.
The liquid condenses in a vanishing part of the total volume but takes most of
the mass of the system. However, the gaseous phase, which mass grows only
logarithmically with the system size, is relevant because its fast particles
carry most of the energy of the system. Remarkably, the system self-organizes
to dissipate no energy: the inelastic decay of energy is a power-law
$[1+t/t_c]^{-2}$ where $t_c$ diverges in the thermodynamic limit. This behavior
is caused by unusual spatial distribution of particles: on approach to one of
the container's walls the density grows inversely with the distance. We discuss
the relation of our results to the recently proposed finite-time singularity in
other container's geometries.
