ABSTRACT
This paper deals with the chemotaxis system with general sensitivity function:
under homogeneous Neumann boundary conditions in a bounded domain with smooth boundary. Here, and the initial function and the sensitivity function satisfy:
We prove that the classical solutions to the above system are uniformly in-time-bounded provided that there exists a smooth positive function such that for some and the following differential inequality holds
where and is bounded from above. We also present our results for the special case with and These results coincide with the results obtained by Fujie et al. [Math Methods Appl Sci. 2015] in the case of and extend their results in the case of .
AMS SUBJECT CLASSIFICATION:
Acknowledgements
The authors would like to thank the anonymous referees for their careful reading and valuable suggestions on this article.
Notes
No potential conflict of interest was reported by the authors.