Blowup of solutions to a two-chemical substances chemotaxis system in the critical dimension

Kentarou Fujie, Takasi Senba

研究成果: Article査読

13 被引用数 (Scopus)

抄録

This paper deals with positive solutions of the fully parabolic system {ut=Δu−χ∇⋅(u∇v)inΩ×(0,∞),τ1vt=Δv−v+winΩ×(0,∞),τ2wt=Δw−w+uinΩ×(0,∞) under mixed boundary conditions (no-flux and Dirichlet conditions) in a smooth bounded convex domain Ω⊂R4 with positive parameters τ12,χ>0 and nonnegative smooth initial data (u0,v0,w0). Global existence and boundedness of solutions were shown if ‖u0L1(Ω)<(8π)2/χ in Fujie–Senba (2017). In the present paper, it is shown that there exist blowup solutions satisfying ‖u0L1(Ω)>(8π)2/χ. This result suggests that the system can be regard as a generalization of the Keller–Segel system, which has 8π/χ-dichotomy. The key ingredients are a Lyapunov functional and quantization properties of stationary solutions of the system in R4.

本文言語English
ページ(範囲)942-976
ページ数35
ジャーナルJournal of Differential Equations
266
2-3
DOI
出版ステータスPublished - 2019 1 15
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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