Global boundedness in the higher-dimensional fully parabolic chemotaxis with weak singular sensitivity and logistic source

2025/03/11 by Minh Le, Le, Minh · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #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.2503.08024

openalex publication_date 2025/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the following chemotaxis system under homogeneous Neumann boundary conditions in a smooth, open, bounded domain Ω⊂ ℝⁿ with n ≥ 3: \begincases u_t = Δu - χ∇ ⋅ ( (u)/(v^k) ∇ v ) + ru - μu², amp; in Ω× (0,T_{\rm max}), v_t = Δv - αv + βu, amp; in Ω× (0,T_{\rm max}), \endcases where k ∈ (0,1), and χ, r, μ, α, β are positive parameters. In this paper, we demonstrate that for suitably smooth initial data, the problem admits a unique nonnegative classical solution that remains globally bounded in time when μ is sufficiently large.

Cited by

• Chemotaxis models with signal-dependent sensitivity and a logistic-type source, I: Boundedness and global existence

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