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On explicit lower bounds and blow-up times in a model of chemotaxis

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  • This paper is concerned with a parabolic Keller-Segel system in $\mathbb{R}^n$, with $n=2$ or $3$, under Neumann boundary conditions. First, important theoretical and general results dealing with lower bounds for blow-up time estimates are summarized and analyzed. Next, a resolution method is proposed and used to both compute the real blow-up times of such unbounded solutions and analyze and discuss some of their properties.
    Mathematics Subject Classification: 35B44, 35K55, 65M06, 65M60, 82C22, 92C17.


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