A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system

Kentarou Fujie, Takasi Senba

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

This paper deals with time-global solutions to the parabolic system {τut = Δu - ∇ · (u∇ χ (ν)) in Ω × (0, ∞), νt = Δν - ν + u in Ω × (0,∞), under the homogeneous Neumann boundary conditions in a bounded and convex domain Ω ⊂ ℝn (n ≥ 2) with smooth boundary ∂Ω. Here τ is a positive parameter, χ is a smooth function on (0,∞) satisfying χ' > 0 and (u0, ν0) is a pair of nonnegative initial data. We will consider the above system as a perturbation of a nonlocal parabolic equation and establish a sufficient condition of the sensitivity function ? for the global existence of solutions under the assumption of smallness of the constant τ.

Original languageEnglish
Pages (from-to)1639-1672
Number of pages34
JournalNonlinearity
Volume31
Issue number4
DOIs
Publication statusPublished - 2018 Mar 12
Externally publishedYes

Keywords

  • chemotaxis
  • sensitivity function
  • time-global existence

ASJC Scopus subject areas

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

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