Generalized Global Supersolutions with Mass Control for Systems with Taxis

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The existence of generalised global supersolutions with a control upon the total mass is established for a wide family of parabolic-parabolic chemotaxis systems and general integrable initial data in any space dimension. It is verified that as long as a supersolution of this sort remains smooth, it coincides with the classical solution. At the same time, the proposed construction provides solvability beyond a blow-up time. The considered class of systems includes the basic form of the Keller-Segel model as well as the case of a chemorepellent.
Original languageEnglish
Pages (from-to)2425-2443
Number of pages19
JournalSIAM Journal on Mathematical Analysis
Issue number3
Publication statusPublished - 13 Jun 2019


  • math.AP
  • 35B45, 92C17, 35D30, 35D99, 35K55


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