On a nonlocal aggregation model with nonlinear diffusion | Zendy

Dong Li | Zendy; Xiaoyi Zhang | Zendy

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On a nonlocal aggregation model with nonlinear diffusion

Author(s) -

Dong Li,

Xiaoyi Zhang

Publication year - 2010

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2010.27.301

Subject(s) - smoothness , nonlinear system , continuation , norm (philosophy) , mathematics , mathematical analysis , physics , computer science , political science , law , programming language , quantum mechanics

We consider a nonlocal aggregation equation with nonlinear diffusion whicharises from the study of biological aggregation dynamics. As a degenerateparabolic problem, we prove the well-posedness, continuation criteria andsmoothness of local solutions. For compactly supported nonnegative smoothinitial data we prove that the gradient of the solution develops$L_x^\infty$-norm blowup in finite time.

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