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

Masaaki Mizukami; Yuya Tanaka

Archivum Mathematicum (2023)

  • Issue: 2, page 215-222
  • ISSN: 0044-8753

Abstract

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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 lack of the production term makes the solution likely to be bounded. Thus, it is expected that there exists a solution of the system with single production such that the species which does not produce the chemical substance remains bounded, whereas the other species blows up. The purpose of this paper is to prove that this conjecture is true.

How to cite

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Mizukami, Masaaki, and Tanaka, Yuya. "Finite-time blow-up in a two-species chemotaxis-competition model with single production." Archivum Mathematicum (2023): 215-222. <http://eudml.org/doc/298967>.

@article{Mizukami2023,
abstract = {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 lack of the production term makes the solution likely to be bounded. Thus, it is expected that there exists a solution of the system with single production such that the species which does not produce the chemical substance remains bounded, whereas the other species blows up. The purpose of this paper is to prove that this conjecture is true.},
author = {Mizukami, Masaaki, Tanaka, Yuya},
journal = {Archivum Mathematicum},
keywords = {chemotaxis; Lotka–Volterra; finite-time blow-up},
language = {eng},
number = {2},
pages = {215-222},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Finite-time blow-up in a two-species chemotaxis-competition model with single production},
url = {http://eudml.org/doc/298967},
year = {2023},
}

TY - JOUR
AU - Mizukami, Masaaki
AU - Tanaka, Yuya
TI - Finite-time blow-up in a two-species chemotaxis-competition model with single production
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 2
SP - 215
EP - 222
AB - 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 lack of the production term makes the solution likely to be bounded. Thus, it is expected that there exists a solution of the system with single production such that the species which does not produce the chemical substance remains bounded, whereas the other species blows up. The purpose of this paper is to prove that this conjecture is true.
LA - eng
KW - chemotaxis; Lotka–Volterra; finite-time blow-up
UR - http://eudml.org/doc/298967
ER -

References

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  7. Stinner, C., Tello, J.I., Winkler, M., 10.1007/s00285-013-0681-7, J. Math. Biol. 68 (7) (2014), 1607–1626. (2014) MR3201907DOI10.1007/s00285-013-0681-7
  8. Tello, J.I., Winkler, M., 10.1088/0951-7715/25/5/1413, Nonlinearity 25 (5) (2012), 1413–1425. (2012) MR2914146DOI10.1088/0951-7715/25/5/1413
  9. Tu, X., Qiu, S., Finite-time blow-up and global boundedness for chemotaxis system with strong logistic dampening, J. Math. Anal. Appl. 486 (1) (2020), 25 pp. (2020) MR4053055
  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

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