On some sharper boundedness conditions in the higher-dimensional chemotaxis-consumption model

2021/09/13 by Silvia Frassu, Frassu, Silvia, Giuseppe Viglialoro +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.2109.06052

openalex publication_date 2021/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the classical zero-flux chemotaxis-consumption model u_t= Δu - χ∇ ⋅ (u ∇ v) \textrmand v_t=Δv- uv, with (x,t)∈ Ω× (0,T_max), Ω being a bounded and smooth domain of ℝⁿ, n≥ 3, χ some positive number and T_max ∈ (0,∞], the following was established in a paper by Tao: for every sufficiently regular initial data u(x,0)=u₀(x)≥ 0 and v(x,0)=v₀(x) ≥ 0, there is χ(‖ v₀ ‖_L^∞(Ω)) such that for all 0

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