A note on construction of nonnegative initial data inducing unbounded solutions to some two-dimensional Keller-Segel systems

Kentaro Fujie, Jie Jiang

Research output: Contribution to journalArticlepeer-review

Abstract

It was shown that unbounded solutions of the Neumann initial-boundary value problem to the two-dimensional Keller-Segel system can be induced by initial data having large negative energy if the total mass Λ ∈ (4π, ∞) \ 4π · N and an example of such an initial datum was given for some transformed system and its associated energy in Horstmann-Wang (2001). In this work, we provide an alternative construction of nonnegative nonradially symmetric initial data enforcing unbounded solutions to the original Keller-Segel model.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalMathematics In Engineering
Volume4
Issue number6
DOIs
Publication statusPublished - 2022

Keywords

  • Chemotaxis
  • Infinite-time blow-up
  • Keller-Segel system
  • Local sensing
  • Lyapunov functional
  • Unbounded solution

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Analysis

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