TY - JOUR

T1 - Finite-time blow-up in the three-dimensional fully parabolic attraction-dominated attraction-repulsion chemotaxis system

AU - Lankeit, Johannes

PY - 2021/12/15

Y1 - 2021/12/15

N2 - We show that the attraction-repulsion chemotaxis system \begin{equation*} \begin{cases} u_t = \Delta u - \chi\nabla\cdot(u\nabla v_1) + \xi\nabla\cdot(u\nabla v_2)\\ \partial_t v_1 = \Delta v_1 - \beta v_1 + \alpha u \\ \partial_t v_2 = \Delta v_2 - \delta v_2 + \gamma u, \end{cases} \end{equation*} posed with homogeneous Neumann boundary conditions in bounded domains \(\Omega=B_R \subset \mathbb{R}^3\), \(R>0\), admits radially symmetric solutions which blow-up in finite time if it is attraction-dominated in the sense that \(\chi\alpha-\xi\gamma>0\).

AB - We show that the attraction-repulsion chemotaxis system \begin{equation*} \begin{cases} u_t = \Delta u - \chi\nabla\cdot(u\nabla v_1) + \xi\nabla\cdot(u\nabla v_2)\\ \partial_t v_1 = \Delta v_1 - \beta v_1 + \alpha u \\ \partial_t v_2 = \Delta v_2 - \delta v_2 + \gamma u, \end{cases} \end{equation*} posed with homogeneous Neumann boundary conditions in bounded domains \(\Omega=B_R \subset \mathbb{R}^3\), \(R>0\), admits radially symmetric solutions which blow-up in finite time if it is attraction-dominated in the sense that \(\chi\alpha-\xi\gamma>0\).

KW - math.AP

KW - 35B44, 92C17, 35Q92, 35K55

KW - Attraction-repulsion

KW - Chemotaxis

KW - Blow-up

UR - http://www.scopus.com/inward/record.url?scp=85108717620&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2103.17044

DO - 10.48550/arXiv.2103.17044

M3 - Article

VL - 504

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

M1 - 125409

ER -