@article{Zheng2024, 
author = {Zihan Zheng and Juan Wang and Liming Cai},
title = {Global boundedness in a Keller-Segel system with nonlinear indirect signal consumption mechanism},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {8},
pages = {4796-4808},
keywords = {chemotaxis system, global boundedness, nonlinear indirect signal},
url = {https://www.sciopen.com/article/10.3934/era.2024219},
doi = {10.3934/era.2024219},
abstract = {In this paper, we study a quasilinear chemotaxis model with a nonlinear indirect consumption mechanism   {v1t=∇⋅(ψ(v1)∇v1−χϕ(v1)∇v2)+λ1v1−λ2v1β,x∈Ω,t>0,v2t=Δv2−wθv2,x∈Ω,t>0,0=Δw−w+v1α,x∈Ω,t>0,in a smooth and bounded domain  Ω⊂Rn(n≥1) with homogeneous Neumann boundary conditions, where  χ,λ1,λ2,θ>0,0<α≤1θ,β≥2,   ψ, and  ϕ are nonlinear functions that satisfy  ψ(s)≥a0(s+1)r1 and  0≤ϕ(s)≤b0s(s+1)r2 for all  s≥0 with  a0,b0>0 and  r1,r2∈R. It has been proven that if  r1>2r2+1, then the problem admits a global and bounded classical solution for some appropriate nonnegative initial data.}
}