Minimal Mass Blowup Solutions for the Patlak-Keller-Segel Equation

Tej Eddine Ghoul; Nader Masmoudi

doi:10.1002/cpa.21787

Minimal Mass Blowup Solutions for the Patlak-Keller-Segel Equation

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Abstract

We consider the parabolic-elliptic Patlak-Keller-Segel (PKS) model of chemotactic aggregation in two space dimensions which describes the aggregation of bacteria under chemotaxis. When the mass is equal to 8π and the second moment is finite (the doubly critical case), we give a precise description of the dynamic as time goes to infinity and extract the limiting profile and speed. The proof shows that this dynamic is stable under perturbations.

Original language	English (US)
Pages (from-to)	1957-2015
Number of pages	59
Journal	Communications on Pure and Applied Mathematics
Volume	71
Issue number	10
DOIs	https://doi.org/10.1002/cpa.21787
State	Published - Oct 2018

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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abstract = "We consider the parabolic-elliptic Patlak-Keller-Segel (PKS) model of chemotactic aggregation in two space dimensions which describes the aggregation of bacteria under chemotaxis. When the mass is equal to 8π and the second moment is finite (the doubly critical case), we give a precise description of the dynamic as time goes to infinity and extract the limiting profile and speed. The proof shows that this dynamic is stable under perturbations.",

author = "Ghoul, {Tej Eddine} and Nader Masmoudi",

note = "Funding Information: Acknowledgments. N. M. was partially supported by NSF grant DMS 1716466. Publisher Copyright: {\textcopyright} 2018 Wiley Periodicals, Inc.",

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AB - We consider the parabolic-elliptic Patlak-Keller-Segel (PKS) model of chemotactic aggregation in two space dimensions which describes the aggregation of bacteria under chemotaxis. When the mass is equal to 8π and the second moment is finite (the doubly critical case), we give a precise description of the dynamic as time goes to infinity and extract the limiting profile and speed. The proof shows that this dynamic is stable under perturbations.

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Minimal Mass Blowup Solutions for the Patlak-Keller-Segel Equation

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