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1 results

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

  • Part of
  • Elio Espejo
  • Journal:
    European Journal of Applied Mathematics , First View
    Published online by Cambridge University Press:
    02 December 2024, pp. 1-38
    • Article
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  • 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.