Boundedness in a quasilinear chemotaxis model with consumption of chemoattractant and logistic source

Abstract

This paper is devoted to the chemotaxis system with logistic source

endowed with homogeneous Neumann boundary conditions and suitable initial conditions, where () is a bounded and smooth domain. Here we assume that

where , , and . Moreover, we will require for all with some , and . Then if one of the following cases hold:

(i)	, where
(ii)	;
(iii)	and b is sufficiently large,

it is proved that the system possesses a unique global bounded classical solution.

Keywords:

• Chemotaxis
• global existence
• boundedness

AMS Subject Classifications:

• 92C17
• 35K55
• 35B40

Acknowledgements

The authors are very grateful to the anonymous reviewers for their carefully reading and valuable suggestions which greatly improved this work.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is supported by the NNSF of China [grant number 11601052]; Doctor Start-up Funding of Chongqing University of Posts and Telecommunications [grant number A2016-24]; the Scientific and Technological Research Program of Chongqing Municipal Education Commission [grant number KJ1600414]; the second author is supported by NNSF of China [grant number 11371384], [grant number 11571062] and Chongqing Natural Science Foundation [grant number cstc2015jcyjBX0007]; the fourth author is supported by the NNSF of China [grant number 11601053].