Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 148, Issue 11, Pages 4855-4873Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/15124
Keywords
Signal-dependent motility; global existence; blow-up; critical mass
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Funding
- NSF of China [11871226]
- Fundamental Research Funds for the Central Universities
- Hong Kong Polytechnic University
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This paper is concerned with the global boundedness and blow-up 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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