Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 47, Issue 5, Pages 1024-1069Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605302.2021.2021422
Keywords
Boundedness; comparison; global existence; stabilization
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Funding
- Hubei Provincial Natural Science Foundation [2020CFB602]
- National Natural Science Foundation of China (NSFC) [11431005]
- Shanghai Science and Technology Committee (STCSM) [18dz2271000]
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This study investigates the well-posedness and uniform-in-time boundedness of a three-component parabolic system describing the dynamics of cell populations interacting with a chemoattractant and a nutrient. The results show that under certain conditions, solutions converge to a spatially homogeneous steady state with an exponential rate for consumption rates behaving linearly near zero. Additionally, growth conditions on the motility function are identified to ensure the uniform-in-time boundedness of solutions.
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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