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Global solutions of a Keller--Segel system with saturated logarithmic sensitivity function

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  • We study a Keller-Segel type chemotaxis model with a modified sensitivity function in a bounded domain $\Omega\subset \mathbb{R}^N$, $N\geq2$. The global existence of classical solutions to the fully parabolic system is established provided that the ratio of the chemotactic coefficient to the motility of cells is not too large.
    Mathematics Subject Classification: Primary: 92C17, 35B32, 35B35, 35B36, 35B40, 35J47.


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