GLOBAL EXISTENCE, UNIFORM BOUNDEDNESS, AND STABILIZATION IN A CHEMOTAXIS SYSTEM WITH DENSITY-SUPPRESSED MOTILITY AND NUTRIENT CONSUMPTION - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Communications in Partial Differential Equations Année : 2022

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

Résumé

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.
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Dates et versions

hal-03247391 , version 1 (03-06-2021)

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Citer

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⟩
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