Global existence, uniform boundedness, and stabilization in a chemotaxis system with density-suppressed motility and nutrient consumption

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...

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Published inCommunications in partial differential equations Vol. 47; no. 5; pp. 1024 - 1069
Main Authors Jiang, Jie, Laurençot, Philippe, Zhang, Yanyan
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 04.05.2022
Taylor & Francis Ltd
Subjects
Analysis of PDEs
Boundedness
comparison
Consumption
Density
global existence
Mathematics
Motility
stabilization
Well posed problems
global existence
comparison
stabilization
boundedness
Online AccessGet full text
ISSN0360-5302
1532-4133
DOI10.1080/03605302.2021.2021422

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Abstract 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.
AbstractList 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.
Author Jiang, Jie
Laurençot, Philippe
Zhang, Yanyan
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  fullname: Laurençot, Philippe
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  givenname: Yanyan
  surname: Zhang
  fullname: Zhang, Yanyan
  organization: School of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University
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Snippet Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics of a...
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SubjectTerms Analysis of PDEs
Boundedness
comparison
Consumption
Density
global existence
Mathematics
Motility
stabilization
Well posed problems
Title Global existence, uniform boundedness, and stabilization in a chemotaxis system with density-suppressed motility and nutrient consumption
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