  We consider a nonlocal aggregation equation with nonlinear diffusion which
arises from the study of biological aggregation dynamics. As a degenerate
parabolic problem, we prove the well-posedness, continuation criteria and
smoothness of local solutions. For compactly supported nonnegative smooth
initial data we prove that the gradient of the solution develops
$L_x^\infty$-norm blowup in finite time.
