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 languageEnglish (US)
Pages (from-to)1957-2015
Number of pages59
JournalCommunications on Pure and Applied Mathematics
Volume71
Issue number10
DOIs
StatePublished - Oct 2018

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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