Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity

This article concerns the quasilinear fully parabolic attraction-repulsion chemotaxis system $$\displaylines{ u_t=\nabla \cdot ((u+1)^{m-1}\nabla u -\chi u(u+1)^{p-2} \nabla v + \xi u(u+1)^{p-2}\nabla w),\quad x \in \Omega,\; t >0,\cr v_t=\Delta v+\alpha u-\beta v, \quad x \in \Omega,\; t >0,\...

Full description

Saved in:
Bibliographic Details
Main Authors: Yutaro Chiyo, Takeshi Uemura, Tomomi Yokota
Format: Article
Language:English
Published: Texas State University 2025-08-01
Series:Electronic Journal of Differential Equations
Subjects:
Online Access:http://ejde.math.txstate.edu/Volumes/2025/81/abstr.html
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849341265727979520
author Yutaro Chiyo
Takeshi Uemura
Tomomi Yokota
author_facet Yutaro Chiyo
Takeshi Uemura
Tomomi Yokota
author_sort Yutaro Chiyo
collection DOAJ
description This article concerns the quasilinear fully parabolic attraction-repulsion chemotaxis system $$\displaylines{ u_t=\nabla \cdot ((u+1)^{m-1}\nabla u -\chi u(u+1)^{p-2} \nabla v + \xi u(u+1)^{p-2}\nabla w),\quad x \in \Omega,\; t >0,\cr v_t=\Delta v+\alpha u-\beta v, \quad x \in \Omega,\; t >0,\cr w_t=\Delta w+\gamma u-\delta w, \quad x \in \Omega,\; t >0 }$$ with homogeneous Neumann boundary conditions, where $\Omega \subset \mathbb{R}^n$ $(n \in \{2,3\})$ is an open ball, $m, p \in \mathbb{R}$, $\chi, \xi, \alpha, \beta, \gamma, \delta >0$ are constants. The main result asserts finite-time blow-up of solutions to this system with some positive initial data when $\chi\alpha-\xi\gamma >0$, $p \ge 2$ and $p-m >2/n$.
format Article
id doaj-art-11806d109acc45e4841365d006c25aed
institution Kabale University
issn 1072-6691
language English
publishDate 2025-08-01
publisher Texas State University
record_format Article
series Electronic Journal of Differential Equations
spelling doaj-art-11806d109acc45e4841365d006c25aed2025-08-20T03:43:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912025-08-01202581,110Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivityYutaro Chiyo0Takeshi Uemura1Tomomi Yokota2 Tokyo Univ. of Science, Tokyo, Japan Tokyo Univ. of Science, Tokyo, Japan Tokyo Univ. of Science, Tokyo, Japan This article concerns the quasilinear fully parabolic attraction-repulsion chemotaxis system $$\displaylines{ u_t=\nabla \cdot ((u+1)^{m-1}\nabla u -\chi u(u+1)^{p-2} \nabla v + \xi u(u+1)^{p-2}\nabla w),\quad x \in \Omega,\; t >0,\cr v_t=\Delta v+\alpha u-\beta v, \quad x \in \Omega,\; t >0,\cr w_t=\Delta w+\gamma u-\delta w, \quad x \in \Omega,\; t >0 }$$ with homogeneous Neumann boundary conditions, where $\Omega \subset \mathbb{R}^n$ $(n \in \{2,3\})$ is an open ball, $m, p \in \mathbb{R}$, $\chi, \xi, \alpha, \beta, \gamma, \delta >0$ are constants. The main result asserts finite-time blow-up of solutions to this system with some positive initial data when $\chi\alpha-\xi\gamma >0$, $p \ge 2$ and $p-m >2/n$.http://ejde.math.txstate.edu/Volumes/2025/81/abstr.htmlfinite-time blow-upquasilinearattraction-repulsionchemotaxis
spellingShingle Yutaro Chiyo
Takeshi Uemura
Tomomi Yokota
Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity
Electronic Journal of Differential Equations
finite-time blow-up
quasilinear
attraction-repulsion
chemotaxis
title Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity
title_full Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity
title_fullStr Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity
title_full_unstemmed Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity
title_short Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity
title_sort finite time blow up in a quasilinear fully parabolic attraction repulsion chemotaxis system with density dependent sensitivity
topic finite-time blow-up
quasilinear
attraction-repulsion
chemotaxis
url http://ejde.math.txstate.edu/Volumes/2025/81/abstr.html
work_keys_str_mv AT yutarochiyo finitetimeblowupinaquasilinearfullyparabolicattractionrepulsionchemotaxissystemwithdensitydependentsensitivity
AT takeshiuemura finitetimeblowupinaquasilinearfullyparabolicattractionrepulsionchemotaxissystemwithdensitydependentsensitivity
AT tomomiyokota finitetimeblowupinaquasilinearfullyparabolicattractionrepulsionchemotaxissystemwithdensitydependentsensitivity