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Minimal Mass Blowup Solutions for the Patlak‐Keller‐Segel Equation
Author(s) -
Ghoul TejEddine,
Masmoudi Nader
Publication year - 2018
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21787
Subject(s) - infinity , limiting , mathematics , critical mass (sociodynamics) , moment (physics) , space (punctuation) , chemotaxis , mathematical analysis , computer science , physics , classical mechanics , mechanical engineering , social science , biochemistry , chemistry , receptor , sociology , engineering , operating system
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. © 2018 Wiley Periodicals, Inc.