Communications on Pure and Applied Analysis (CPAA)

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

Pages: 1617 - 1637, Volume 9, Issue 6, November 2010      doi:10.3934/cpaa.2010.9.1617

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Andrea L. Bertozzi - Department of Mathematics, UCLA, Los Angeles, CA, 90095, United States (email)
Dejan Slepcev - Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA, 15213, United States (email)

Abstract: 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, 92D50.

Received: October 2009;      Revised: May 2010;      Available Online: August 2010.