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

2021/03/31 by Johannes Lankeit, Lankeit, Johannes
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #35B44 #35K55 #35Q92 #92C17 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2103.17044

openalex publication_date 2021/03/31 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We show that the attraction-repulsion chemotaxis system n
begincases u_t =
Delta u -
chi
nabla
cdot(u
nabla v₁) +\n
xi
nabla
cdot(u
nabla v₂)

\n
partial_t v₁ =
Delta v₁ -
beta v₁ +
alpha u

\n
partial_t v₂ =
Delta v₂ -
delta v₂ +
gamma u,
endcases\n posed with homogeneous Neumann boundary conditions in bounded\ndomains \Ω=B_R \⊂ \ℝ³, R>0, admits radially symmetric\nsolutions which blow-up in finite time if it is attraction-dominated in the\nsense that \χ\α-\ξ\γ>0.\n

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