A note on boundedness of solutions to a higher‐dimensional quasi–linear chemotaxis system with logistic source

Abstract

We deal with the boundedness of solutions of a class of quasilinear chemotaxis systems generalizing the prototype urn:x-wiley:00442267:media:zamm201600166:zamm201600166-math-0001where is a bounded domain with smooth boundary, , . It is showed that if , then for any sufficiently smooth initial data there exists a classical solution which is global in time and bounded. The novelty of the paper is that we use the boundedness of to estimate the boundedness of which is different from and . The results of this paper partly improve the results of and .