# American Institute of Mathematical Sciences

February  2010, 27(1): 301-323. doi: 10.3934/dcds.2010.27.301

## On a nonlocal aggregation model with nonlinear diffusion

 1 Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, United States, United States

Received  April 2009 Revised  December 2009 Published  February 2010

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.
Citation: Dong Li, Xiaoyi Zhang. On a nonlocal aggregation model with nonlinear diffusion. Discrete & Continuous Dynamical Systems - A, 2010, 27 (1) : 301-323. doi: 10.3934/dcds.2010.27.301
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