Global existence and boundedness in a chemotaxis-convection model with sensitivity functions for tumor angiogenesis

2023/04/24 by Yutaro Chiyo, Chiyo, Yutaro, Masaaki Mizukami +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #35A01 #35Q92 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics #Kruppel-like factors research #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2304.11800

openalex publication_date 2023/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with the fully parabolic chemotaxis-convection model with sensitivity functions for tumor angiogenesis, \begincases u_t=Δu-∇ ⋅ (uχ₁(v)∇ v) +∇ ⋅ (uχ₂(w)∇ w), amp;x ∈ Ω, tgt;0,
v_t=Δv+∇ ⋅ (vξ(w)∇ w)+αu-βv, amp;x ∈ Ω, tgt;0,
w_t=Δw+γu-δw, amp;x ∈ Ω, tgt;0 \endcases under homogeneous Neumann boundary conditions and initial conditions, where Ω⊂ ℝⁿ (n ≤ 3) is a bounded domain with smooth boundary, χ₁, χ₂, ξ are functions satisfying some conditions and α, β, γ, δ>0 are constants. The purpose of this paper is to establish global existence and boundedness in this system.

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