Stabilization in a chemotaxis model for tumor invasion

Kentarou Fujie, Akio Ito, Michael Winkler, Tomomi Yokota

Research output: Contribution to journalArticlepeer-review

63 Citations (Scopus)


This paper deals with the chemotaxis system {ut = δu -δ · (uδv), x Isin; ω, t > 0, vt = δv + wz, x ∈ ω, t > 0, wt = -wz, x ∈ ω, t > 0, zt = δz -z + u, x ∈ ω, t > 0, in a sm∞thly bounded domain ω ∪ Rn, n < 3, that has recently been proposed as a model for tumor invasion in which the role of an active extracellular matrix is accounted for. It is shown that for any choice of nonnegative and suitably regular initial data (uo, vo, wo, zo), a corresponding initial-boundary value problem of Neumann type possesses a global solution which is bounded. Moreover, it is proved that whenever uo ^ 0, these solutions approach a certain spatially homogeneous equilibrium in the sense that as t → ∞, u(x, t) → u0, v(x,t) → v0 + w0, w(x,t) → 0 and z(x,t) → u0, uniformly with respect to x ∈ ω, where u0 := 1/|ω|∫ω u0, v0 := 1/|ω|∫ω u0 and w0 := 1/ω|∫ω w0.

Original languageEnglish
Pages (from-to)151-169
Number of pages19
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number1
Publication statusPublished - 2016 Jan 1
Externally publishedYes


  • Asymptotic behavior
  • Chemotaxis
  • Tumor invasion

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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