This article concerns the attraction-repulsion chemotaxis system with nonlinear diffusion and logistic source,
under Neumann boundary conditions in a bounded domain with smooth boundary. We show that if the diffusion is strong enough or the logistic dampening is sufficiently powerful, then the corresponding system possesses a global bounded classical solution for any sufficiently regular initial data. Moreover, it is proved that if , and for the latter case, then , and in as .
Submitted February 8, 2016. Published July 6, 2016.
Math Subject Classifications: 35K55, 35Q35, 35Q92, 92C17.
Key Words: Chemotaxis; attraction-repulsion; boundedness; nonlinear diffusion; logistic source.
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| Yilong Wang |
School of Sciences
Southwest Petroleum University
Chengdu 610500, China
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