Mathematical Biology Tumor Growth
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Abstract
Abstract
This paper deals with the following Neumann initial-boundary value problem {ut=Δu−∇⋅(u∇υ)+uγ−uα(∫Ωuβ)m,x∈Ω,t∈(0,Tmax),υt=Δυ−υ+uη,x∈Ω,t∈(0,Tmax),where Ω⊂RN (N≥ 2) is a bounded domain with smooth boundary, 0 1, 1 0. The initial data satisfy u0,υ0∈W1,∞(Ω),where u0≥ 0, υ0≥ 0, and ∂νu0=∂νυ0=0 on ∂Ω. We rigorously prove that the problem admits a unique global classical solution which is uniformly bounded in time if one of the following conditions holds: α+mβ>(N+2)γ−N2 when γ≥η+1,or α+mβ>(N+2)η+22 when γ<η+1.
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@article{Akkoyunlu2026Global,
title = {Global boundedness to a chemotaxis system with modified nonlocal and nonlinear reaction},
author = {Ebubekir Akkoyunlu},
journal = {Applicable Analysis},
year = {2026},
doi = {10.1080/00036811.2026.2707162},
url = {https://doi.org/10.1080/00036811.2026.2707162}
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