2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219584We 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.Submitted Jun 2008Mathematical Physicstext