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Existence of blow-up solutions for a degenerate parabolic-elliptic Keller–Segel system with logistic source

Yuya Tanaka (2023)

Archivum Mathematicum

This paper deals with existence of finite-time blow-up solutions to a degenerate parabolic–elliptic Keller–Segel system with logistic source. Recently, finite-time blow-up was established for a degenerate Jäger–Luckhaus system with logistic source. However, blow-up solutions of the aforementioned system have not been obtained. The purpose of this paper is to construct blow-up solutions of a degenerate Keller–Segel system with logistic source.

Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data

Piotr Biler, Jacek Zienkiewicz (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than 8π as the initial data is given. This result was obtained by Senba and Suzuki (2002) and Bedrossian and Masmoudi (2014) using different arguments. Moreover, we show a uniform bound for the existence time of solutions as well as an optimal hypercontractivity estimate.

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