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

Yuya Tanaka

Archivum Mathematicum (2023)

  • Issue: 2, page 223-230
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Tanaka, Yuya. "Existence of blow-up solutions for a degenerate parabolic-elliptic Keller–Segel system with logistic source." Archivum Mathematicum (2023): 223-230. <http://eudml.org/doc/298990>.

@article{Tanaka2023,
abstract = {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.},
author = {Tanaka, Yuya},
journal = {Archivum Mathematicum},
keywords = {degenerate Keller–Segel system; logistic source},
language = {eng},
number = {2},
pages = {223-230},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Existence of blow-up solutions for a degenerate parabolic-elliptic Keller–Segel system with logistic source},
url = {http://eudml.org/doc/298990},
year = {2023},
}

TY - JOUR
AU - Tanaka, Yuya
TI - Existence of blow-up solutions for a degenerate parabolic-elliptic Keller–Segel system with logistic source
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 2
SP - 223
EP - 230
AB - 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.
LA - eng
KW - degenerate Keller–Segel system; logistic source
UR - http://eudml.org/doc/298990
ER -

References

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  2. Fuest, M., 10.1088/1361-6544/ab7294, Nonlinearity 33 (5) (2020), 2306–2334. (2020) MR4105360DOI10.1088/1361-6544/ab7294
  3. Fuest, M., Approaching optimality in blow-up results for Keller-Segel systems with logistic-type dampening, NoDEA Nonlinear Differential Equations Appl. 28 (16) (2021), 17 pp. (2021) MR4223515
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  5. Ishida, S., Yokota, T., Blow-up in finite or infinite time for quasilinear degenerate Keller–Segel systems of parabolic–parabolic type, Discrete Contin. Dyn. Syst. Ser. B 18 (10) (2013), 2569–2596. (2013) MR3124753
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  7. Tanaka, Y., 10.1016/j.jmaa.2021.125654, J. Math. Anal. Appl. 506 (2022), 29 pp., no. 125654. (2022) MR4315564DOI10.1016/j.jmaa.2021.125654
  8. Tanaka, Y., Yokota, T., 10.3934/dcdsb.2022075, Discrete Contin. Dyn. Syst. Ser. B 28 (1) (2023), 262–286. (2023) MR4489725DOI10.3934/dcdsb.2022075
  9. Winkler, M., 10.1016/j.jmaa.2011.05.057, J. Math. Anal. Appl. 384 (2) (2011), 261–272. (2011) MR2825180DOI10.1016/j.jmaa.2011.05.057
  10. Winkler, M., Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation, Z. Angew. Math. Phys. 69 (69) (2018), 40 pp. (2018) MR3772030
  11. Winkler, M., Djie, K.C., 10.1016/j.na.2009.07.045, Nonlinear Anal. 72 (2) (2010), 1044–1064. (2010) MR2579368DOI10.1016/j.na.2009.07.045

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