Volume 43 Issue 7
Jul.  2022
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LI Yuanfei. Global Existence of Solutions and Lower Bound Estimate of Blow-Up Time for the Keller-Segel Chemotaxis Model[J]. Applied Mathematics and Mechanics, 2022, 43(7): 816-824. doi: 10.21656/1000-0887.420109
Citation: LI Yuanfei. Global Existence of Solutions and Lower Bound Estimate of Blow-Up Time for the Keller-Segel Chemotaxis Model[J]. Applied Mathematics and Mechanics, 2022, 43(7): 816-824. doi: 10.21656/1000-0887.420109

Global Existence of Solutions and Lower Bound Estimate of Blow-Up Time for the Keller-Segel Chemotaxis Model

doi: 10.21656/1000-0887.420109
  • Received Date: 2021-04-25
  • Rev Recd Date: 2021-07-08
  • Publish Date: 2022-07-15
  • A macroscopic nonlinear Keller-Segel model for chemotactic cell migration was considered, where the existence region of the model is a bounded convex one on$\varOmega\subset\mathbb{R}^N(N\geqslant2)$. The global existence of the solution on $\varOmega\subset\mathbb{R}^3$ was obtained by means of the energy estimate method. The lower bound of the blow-up time was proved for $N=3 $ and $N=2$.

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