TY - JOUR
T1 - Analysis of a model describing bacterial colony expansion in radial geometry driven by chemotaxis
AU - Espejo, Elio
N1 - Publisher Copyright:
© The Author(s), 2024.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - blow-up
KW - fluids
KW - modified Darcy's law
KW - Moser-Trudinger inequality
KW - source
UR - http://www.scopus.com/inward/record.url?scp=85210968853&partnerID=8YFLogxK
U2 - 10.1017/S0956792524000809
DO - 10.1017/S0956792524000809
M3 - Article
AN - SCOPUS:85210968853
SN - 0956-7925
JO - European Journal of Applied Mathematics
JF - European Journal of Applied Mathematics
ER -