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

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Jie Jiang, P. Laurençot, Yanyan Zhang
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引用次数: 12

Abstract

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.
具有密度抑制运动和营养消耗的趋化系统的整体存在性、均匀有界性和稳定性
摘要研究了一个描述细胞群体与化学引诱剂和营养物相互作用动力学的三组分抛物型系统的经典解的适定性和时界一致性。前者在细胞的扩散运动中诱导趋化偏向,并通过密度抑制的运动来解释。首先建立了在无穷远处消失的一般正运动函数和非递增运动函数的适定性。其次,确定了保证解在时间上一致有界性的运动函数的增长条件。最后,对于亚线性衰减的运动函数,显示了收敛到空间齐次稳态,消耗率的指数速率在接近零的地方线性表现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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