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Semigroup and Blow-up Dynamics of Attraction Keller-Segel Equations in Scale of Banach Spaces

Volume 21, Number 1 (2018), 1 - 31

Semigroup and Blow-Up Dynamics of Attraction Keller-Segel Equations in Scale of Banach Spaces

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Abstract

In this paper, we study the asymptotic and blow-up dynamics of the attraction Keller-Segel chemotaxis system of equations in scale of Banach spaces $E_{q}^{\alpha}=H^{2\alpha,q}(\Omega)$, $-1\leq \alpha\leq 1, 10$, if the chemo-attractivity coefficient dominates the Moser-Trudinger threshold value. An analysis of the finite time bounds for blow-up of solutions in norm of $L^{2p}(\Omega), 1\leq p\leq 6$ and $\Omega\subset {\mathbb R}^{N}, N=2,3$, is also furnished.