## 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_{∗}

Original language | English |
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Pages (from-to) | 4855-4873 |

Number of pages | 19 |

Journal | Proceedings of the American Mathematical Society |

Volume | 148 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 2020 |

## Keywords

- Blow-up
- Critical mass
- Global existence
- Signal-dependent motility

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics