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Lower bounds for blow-up in a parabolic-parabolic Keller-Segel system

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  • This paper deals with a parabolic-parabolic Keller-Segel system, modeling chemotaxis, with time dependent coefficients. We consider non-negative solutions of the system which blow up in finite time $t^*$ and an explicit lower bound for $t^*$ is derived under sufficient conditions on the coefficients and the spatial domain.
    Mathematics Subject Classification: Primary: 35K55, 35B44. Secondary: 92C17.


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