Global existence of solutions to a parabolic-elliptic system of drift-diffusion type in R2

Toshitaka Nagai, Takayoshi Ogawa

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We consider the Cauchy problem of a parabolic-elliptic system in R2, which appears in various fields in physics and biology. Under a mild restriction on the initial data, we show the global existence of nonnegative solutions to the Cauchy problem for both the subcritical and the critical cases, that is, the total mass of the solution is less than or equal to 8π.

Original languageEnglish
Pages (from-to)67-112
Number of pages46
JournalFunkcialaj Ekvacioj
Volume59
Issue number1
DOIs
Publication statusPublished - 2016 Apr 14

Keywords

  • Chemotaxis model
  • Global existence
  • Gravitational model
  • Interaction particle
  • Subcritical case
  • Two dimensions

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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