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- W4283644817 abstract "This paper is concerned with global solvability of a fully parabolic system of Keller--Segel-type involving non-monotonic signal-dependent motility. First, we prove global existence of classical solutions to our problem with generic positive motility function under a certain smallness assumption at infinity, which however permits the motility function to be arbitrarily large within a finite region. Then uniform-in-time boundedness of classical solutions is established whenever the motility function has strictly positive lower and upper bounds in any dimension $Ngeq1$, or decays at a certain slow rate at infinity for $Ngeq2$. Our results remove the crucial non-increasing requirement on the motility function in some recent work cite{JLZ22,FJ19b,FS22} and hence allow for both chemo-attractive and chemo-repulsive effect, or their co-existence in applications. The key ingredient of our proof lies in an important improvement of the comparison method developed in cite{JLZ22,FJ19b,LJ21}." @default.
- W4283644817 created "2022-06-29" @default.
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- W4283644817 date "2022-06-24" @default.
- W4283644817 modified "2023-09-25" @default.
- W4283644817 title "Global Existence and Uniform Boundedness in a Fully Parabolic Keller-Segel System with Non-monotonic Signal-dependent Motility" @default.
- W4283644817 doi "https://doi.org/10.48550/arxiv.2206.12196" @default.
- W4283644817 hasPublicationYear "2022" @default.
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