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arXiv · 1911.05340

Critical mass on the Keller-Segel system with signal-dependent motility

Hai-Yang Jin·Zhi-An Wang
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Abstract

This paper is concerned with the global boundedness and blowup of solutions to the Keller-Segel system with density-dependent motility in a two-dimensional bounded smooth domain with Neumman boundary conditions. We show that if the motility function decays exponentially, then a critical mass phenomenon similar to the minimal Keller-Segel model will arise. That is there is a number $m_*>0$, such that the solution will globally exist with uniform-in-time bound if the initial cell mass (i.e. $L^1$-norm of the initial value of cell density) is less than $m_*$, while the solution may blow up if the initial cell mass is greater than $m_*$.

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Hai-Yang Jin, Zhi-An Wang. 2019-11-13. Critical mass on the Keller-Segel system with signal-dependent motility. https://doi.org/10.1090/proc%2F15124

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