  We consider the aggregation equation $u_t= \div(\nabla u-u\nabla \K(u))$ in a
bounded domain $\Omega\subset \R^d$ with supplemented the Neumann boundary
condition and with a nonnegative, integrable initial datum. Here, $\K=\K(u)$ is
an integral operator. We study the local and global existence of solutions and
we derive conditions which lead us to either the stability or instability of
constant solutions.
