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On a nonlocal aggregation model with nonlinear diffusion
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.