GLOBAL EXISTENCE, UNIFORM BOUNDEDNESS, AND STABILIZATION IN A CHEMOTAXIS SYSTEM WITH DENSITY-SUPPRESSED MOTILITY AND NUTRIENT CONSUMPTION

Jie Jiang (1) , Philippe Laurençot (2) , Yanyan Zhang (3)

1 Chinese Academy of Sciences [Wuhan Branch]
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 ECNU - East China Normal University [Shangaï]

Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics of a population of cells interacting with a chemoattractant and a nutrient. The former induces a chemotactic bias in the diffusive motion of the cells and is accounted for by a density-suppressed motility. Well-posedness is first established for generic positive and non-increasing motility functions vanishing at infinity. Growth conditions on the motility function guaranteeing the uniform-in-time boundedness of solutions are next identified. Finally, for sublinearly decaying motility functions, convergence to a spatially homogeneous steady state is shown, with an exponential rate for consumption rates behaving linearly near zero.

Mots clés: global existence; boundedness; comparison; stabilization

Domaines: Equations aux dérivées partielles [math.AP]

Jie Jiang, Philippe Laurençot, Yanyan Zhang. GLOBAL EXISTENCE, UNIFORM BOUNDEDNESS, AND STABILIZATION IN A CHEMOTAXIS SYSTEM WITH DENSITY-SUPPRESSED MOTILITY AND NUTRIENT CONSUMPTION. Communications in Partial Differential Equations, 2022, 47 (5), pp.1024--1069. ⟨hal-03247391⟩