On a Nonlocal Aggregation Model with Nonlinear Diffusion
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چکیده
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 -norm blowup in finite time.
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تاریخ انتشار 2008