Some remarks on well-posedness of the higher-dimensional chemorepulsion system

Volume 67 / 2019

Tomasz Cieślak, Kentarou Fujie Bulletin Polish Acad. Sci. Math. 67 (2019), 165-178 MSC: 35B45, 35K45, 92C17. DOI: 10.4064/ba190324-4-6 Published online: 14 June 2019


We consider a fully parabolic system of chemorepulsion in higher dimensions. We introduce a new energy-like identity and comment on its relation to the Li–Yau–Hamilton inequalities. Next, we show that for the chemorepellent moving much more slowly than the cells, the time global well-posedness holds.


  • Tomasz CieślakInstitute of Mathematics
    Polish Academy of Sciences
    00-656 Warszawa, Poland
  • Kentarou FujieResearch Alliance Center for Mathematical Sciences
    Tohoku University
    Sendai, 980-8578, Japan

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