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

Andrea L. Bertozzi; Dejan Slepčev

doi:10.3934/cpaa.2010.9.1617

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

Andrea L. Bertozzi
, Dejan Slepčev

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1617-1637
Number of pages	21
Journal	Communications on Pure and Applied Analysis
Volume	9
Issue number	6
DOIs	https://doi.org/10.3934/cpaa.2010.9.1617
Publication status	Published - Nov 2010
Externally published	Yes

Keywords

Aggregation
Nonlocal interaction

Access to Document

10.3934/cpaa.2010.9.1617

https://arrow.tudublin.ie/scschmatart/132Licence: CC BY-NC-SA

Cite this

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title = "Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion",

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",

author = "Bertozzi, \{Andrea L.\} and Dejan Slep{\v c}ev",

year = "2010",

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language = "English",

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journal = "Communications on Pure and Applied Analysis",

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AU - Slepčev, Dejan

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N2 - 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.

AB - 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.

KW - Aggregation

KW - Nonlocal interaction

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U2 - 10.3934/cpaa.2010.9.1617

DO - 10.3934/cpaa.2010.9.1617

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EP - 1637

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

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