Boundedness of solutions to the critical fully parabolic quasilinear one-dimensional Keller–Segel system

Bartosz Bieganowski, Tomasz Cieślak, Kentarou Fujie, Takasi Senba

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper we consider a one-dimensional fully parabolic quasilinear Keller–Segel system with critical nonlinear diffusion. We show uniform-in-time boundedness of solutions, which means, that unlike in higher dimensions, there is no critical mass phenomenon in the case of critical diffusion. To this end we utilize estimates from a well-known Lyapunov functional and a recently introduced new Lyapunov-like functional in.

Original languageEnglish
Pages (from-to)724-732
Number of pages9
JournalMathematische Nachrichten
Volume292
Issue number4
DOIs
Publication statusPublished - 2019 Apr
Externally publishedYes

Keywords

  • Lyapunov-like functional
  • boundedness of solutions
  • chemotaxis

ASJC Scopus subject areas

  • Mathematics(all)

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