2025/06/20 by Mizukami, Masaaki, Tanaka, Yuya
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2506.16752
openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
This paper deals with a problem which describes tuberculosis granuloma formation \begincases ut = Δu - ∇ ⋅ (u ∇ v) - uv - u + β, amp;x ∈ Ω, tgt;0,
vt = Δv + v -uv + μw, amp;x ∈ Ω, tgt;0,
wt = Δw + uv - wz - w, amp;x ∈ Ω, tgt;0,
zt = Δz - ∇ ⋅ (z ∇ w) + f(w)z -z, amp;x ∈ Ω, tgt;0 \endcases under homogeneous Neumann boundary conditions and initial conditions, where Ω⊂ ℝn (n≥ 2) is a smooth bounded domain, β,μ>0 and f is some function, and shows that if initial data are small in some sense then the solution (u,v,w,z) of the problem exists globally and convergences to (β,0,0,0) exponentially when β>1 and the reproduction number R0 := \fracμβ+ 1β satisfies R0<1.