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On a nonlocal aggregation model with nonlinear diffusion

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  • 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.
    Mathematics Subject Classification: Primary: 35K59, 35K65; Secondary: 35Q92.

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