2024/01/31 by Aijing Lu, Jie Jiang, Lu, Aijing +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.2401.17697
openalex publication_date 2024/01/31 · openalex created_date 2024/02/02 · openalex updated_date 2026/07/28
In this paper, we consider an initial-Neumann boundary value problem for a parabolic-elliptic Keller-Segel system with signal-dependent motility and a source term. Previous research has rigorously shown that the source-free version of this system exhibits an infinite-time blowup phenomenon when dimension N ≥ 2. In the current work, when N ≤ 3, we establish uniform boundedness of global classical solutions with an additional source term that involves slightly super-linear degradation effect on the density, of a maximum growth order slog s, unveiling a sufficient blowup suppression mechanism. The motility function considered in our work takes a rather general form compared with recent works \citeFuJi2020, LyWa2023 which were restricted to the monotone non-increasing case. The cornerstone of our proof lies in deriving an upper bound for the second component of the system and an entropy-like estimate, which are achieved through tricky comparison skills and energy methods, respectively.