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

Andrea L. Bertozzi; Dejan Slepcev

doi:10.3934/cpaa.2010.9.1617

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2010, Volume 9, Issue 6: 1617-1637. Doi: 10.3934/cpaa.2010.9.1617 open access

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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
2.
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA, 15213

Received: September 30, 2009

Revised: April 30, 2010

Published: October 2010

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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.

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