Global existence and boundedness of radial solutions to a two dimensional fully parabolic chemotaxis system with general sensitivity

Kentarou Fujie, Takasi Senba

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)

Abstract

This paper deals with positive radially symmetric solutions of the Neumann boundary value problem for the fully parabolic chemotaxis system, in a ball R ω R2 with general sensitivity function x v satisfying x> R 0 and decaying property x'(s) →0 (s→∞ ), parameter ( τ e (0, 1) and nonnegative radially symmetric initial data. It is shown that if (0, 1) is sufficiently small, then the problem has a unique classical radially symmetric solution, which exists globally and remains uniformly bounded in time. Especially, this result establishes global existence of solutions in the case x (v)= x0 log 0 for all x>0 0 , which has been left as an open problem.

Original languageEnglish
Pages (from-to)2417-2450
Number of pages34
JournalNonlinearity
Volume29
Issue number8
DOIs
Publication statusPublished - 2016 Jul 4
Externally publishedYes

Keywords

  • Chemotaxis
  • boundedness
  • global existence
  • logarithmic sensitivity

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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