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November  2010, 9(6): 1617-1637. doi: 10.3934/cpaa.2010.9.1617

Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion

Andrea L. Bertozzi 1, and  Dejan Slepcev 2,

1. 

Department of Mathematics, UCLA, Los Angeles, CA, 90095, United States
2. 

Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA, 15213, United States

Received  October 2009 Revised  May 2010 Published  August 2010

We present an energy-methods-based proof of the existence and uniqueness of solutions of a nonlocal aggregation equation with degenerate diffusion. The equation we study is relevant to models of biological aggregation.
Keywords: Aggregation, nonlocal interaction..
Mathematics Subject Classification: 35K55, 45K05, 35K15, 35K20, 92D5.
Citation: Andrea L. Bertozzi, Dejan Slepcev. Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1617-1637. doi: 10.3934/cpaa.2010.9.1617
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