Brezis-Merle inequalities and application to the global existence of the cauchy problem of the Keller-Segel system

Toshitaka Nagai, Takayoshi Ogawa

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

We discuss the existence of the global solution for two types of nonlinear parabolic systems called the Keller-Segel equation and attractive drift-diffusion equation in two space dimensions. We show that the system admits a unique global solution in Lloc(0, ∞ L (ℝ2)). The proof is based upon the BrezisMerle type inequalities of the elliptic and parabolic equations. The proof can be applied to the Cauchy problem which is describing the self-interacting system.

Original languageEnglish
Pages (from-to)795-812
Number of pages18
JournalCommunications in Contemporary Mathematics
Volume13
Issue number5
DOIs
Publication statusPublished - 2011 Oct

Keywords

  • Brezis-Merle inequalities
  • Keller-Segel system
  • global solutions

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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