2024/05/27 by Fengxiang Zhao, Zhao, Fengxiang, Jiashan Zheng +3
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #MRI in cancer diagnosis #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.2405.17186
openalex publication_date 2024/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the following parabolic-parabolic-elliptic system \\aligned amp; ut=Δu-∇⋅(u∇ v)+ξ∇⋅(u∇ w)+au-μuα, amp;amp; x∈Ω, tgt;0,
amp; vt=Δv+∇⋅(v∇ w)-v+u,amp;amp; x∈Ω, tgt;0,
amp; 0=Δw-w+u,amp;amp; x∈Ω, tgt;0
\endaligned. on a bounded domain Ω⊂ ℝN (N≥1) with smooth boundary ∂ Ω, where μ, a, α are positive constants and ξ∈ℝ. If one of the following cases holds: (i) N≥4 and α>(4N-4+N√(2N2-6N+8))/(2N); (ii) N=3, α>2, for any μ>0 or α=2, the index μ should be suitably big; (iii) N=2, α≥2, for any μ>0. Without any restriction on the index ξ, for any given suitably regular initial data, the corresponding Neumann initial-boundary problem admits a unique global and bounded classical solution.