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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.

Finite-time blow-up in a two-species chemotaxis-competition model with single production

Masaaki Mizukami;  Yuya Tanaka — 2023

Archivum Mathematicum

This paper is concerned with blow-up of solutions to a two-species chemotaxis-competition model with production from only one species. In previous papers there are a lot of studies on boundedness for a two-species chemotaxis-competition model with productions from both two species. On the other hand, finite-time blow-up was recently obtained under smallness conditions for competitive effects. Now, in the biological view, the production term seems to promote blow-up phenomena; this implies that the...

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