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arXiv · 1609.03935

Suppression of blow up by a logistic source in $2$D Keller-Segel system with fractional dissipation

Jan Burczak·Rafael Granero-Belinchón
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Abstract

We consider a two dimensional parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order $\alpha$. We obtain existence of global in time regular solution for arbitrary initial data with no size restrictions and $c<\alpha\leq 2$, where $c \in (0,2)$ depends on the equation's parameters. For an even wider range of $\alpha's$, we prove existence of global in time weak solution for general initial data.

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Jan Burczak, Rafael Granero-Belinchón. 2016-09-13. Suppression of blow up by a logistic source in $2$D Keller-Segel system with fractional dissipation. https://arxiv.org/abs/1609.03935

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