Analysis of a model describing bacterial colony expansion in radial geometry driven by chemotaxis

Research output: Journal PublicationArticlepeer-review

Abstract

We investigate a recent model proposed in the literature elucidating patterns driven by chemotaxis, similar to viscous fingering phenomena. Notably, this model incorporates a singular advection term arising from a modified formulation of Darcy's law. It is noteworthy that this type of advection can also be well interpreted as a description of a radial fluid flow source surrounding an aggregation of cells. For the two-dimensional scenario, we establish a precise threshold delineating between blow-up and global solution existence. This threshold is contingent upon the pressure magnitude and the initial total mass of the aggregating cells.

Original languageEnglish
JournalEuropean Journal of Applied Mathematics
DOIs
Publication statusAccepted/In press - 2024

Keywords

  • blow-up
  • fluids
  • modified Darcy's law
  • Moser-Trudinger inequality
  • source

ASJC Scopus subject areas

  • Applied Mathematics

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