Boundedness and blow-up for quasilinear degenerate Keller-Segel systems with indirect signal production

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发表日期：

2025年7月16日

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Dan Li,
Qian Liu

摘要

In this paper, we investigate the global boundedness and blow-up of solutions to a chemotaxis model with density-dependent motility and split population in a two-dimensional bounded smooth domain with Neumann boundary conditions. We show that if the motility function decays exponentially, when the initial cell mass is less than critical mass $M_{c}$ $M_{c}$ , the solution will globally exist and remain uniformly bounded. Yet initial cell mass over than $M_{c}$ $M_{c}$ , the solution will blow up in finite time.