Global well-posedness of logarithmic Keller-Segel type systems

Jaewook Ahn, Kyungkeun Kang, Jihoon Lee

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We consider a class of logarithmic Keller-Segel type systems modeling the spatio-temporal behavior of either chemotactic cells or criminal activities in spatial dimensions two and higher. Under certain assumptions on parameter values and given functions, the existence of classical solutions is established globally in time, provided that initial data are sufficiently regular. In particular, we enlarge the range of chemotactic sensitivity χ, compared to known results, in case that spatial dimensions are between two and eight. In addition, we provide new type of small initial data to obtain global classical solution, which is also applicable to the urban crime model. We discuss long-time asymptotic behaviors of solutions as well.

Original languageEnglish
Pages (from-to)185-211
Number of pages27
JournalJournal of Differential Equations
Volume287
DOIs
StatePublished - 25 Jun 2021

Keywords

  • Global well-posedness
  • Logarithmic Keller-Segel
  • Urban crime

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