2022/06/24 by Yamin Xiao, Jie Jiang, Xiao, Yamin +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Analysis of PDEs (math.AP) #Bioinformatics and Genomic Networks #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.2206.12196
openalex publication_date 2022/06/24 · openalex created_date 2022/06/29 · openalex updated_date 2026/07/28
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 N≥1, or decays at a certain slow rate at infinity for N≥2. Our results remove the crucial non-increasing requirement on the motility function in some recent work \citeJLZ22,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 \citeJLZ22,FJ19b,LJ21.