On a nonlocal aggregation model with nonlinear diffusion

Details On a nonlocal aggregation model with nonlinear diffusion On a nonlocal aggregation model with nonlinear diffusion

2009-02-12

arxiv.org/abs/0902.2017v1

Physics

Mathematical Physics

Submitted Jun 2008

Scientific paper

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.

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