Generalised supersolutions with mass control for the Keller–Segel system with logarithmic sensitivity

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Abstract

The existence of generalised global supersolutions with a control upon the total muss is established for the parabolic–parabolic Keller–Segel system with logarithmic sensitivity for any space dimension. It is verified that smooth supersolutions of this sort are actually classical solutions. Unlike the previously existing constructions, neither is the chemotactic sensitivity coefficient required to be small, nor is it necessary for the initial data to be radially symmetric.
Original languageEnglish
Pages (from-to)1270-1286
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume467
Issue number2
Early online date02 Aug 2018
DOIs
Publication statusPublished - 15 Nov 2018

Keywords

  • Chemotaxis
  • Generalised supersolution
  • Global existence
  • Logarithmic sensitivity

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