@article{Lyu2022, 
author = {Wenbin Lyu and Zhi-An Wang},
title = {Global classical solutions for a class of reaction-diffusion system with density-suppressed motility},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {3},
pages = {995-1015},
keywords = {boundedness, global existence, reaction-diffusion system, density-suppressed motility},
url = {https://www.sciopen.com/article/10.3934/era.2022052},
doi = {10.3934/era.2022052},
abstract = {This paper is concerned with a class of reaction-diffusion system with density-suppressed motility   {ut=Δ(γ(v)u)+αuF(w),x∈Ω,t>0,vt=DΔv+u−v,x∈Ω,t>0,wt=Δw−uF(w),x∈Ω,t>0,under homogeneous Neumann boundary conditions in a smooth bounded domain  Ω⊂Rn(n≤2), where  α>0 and  D>0 are constants. The random motility function  γ satisfies   γ∈C3((0,+∞)),γ>0,γ′<0on(0,+∞)andlimv→+∞γ(v)=0.The intake rate function  F satisfies  F∈C1([0,+∞)),F(0)=0 and F>0 on (0,+∞). We show that the above system admits a unique global classical solution for all non-negative initial data  u0∈W1,∞(Ω),v0∈W1,∞(Ω),w0∈W1,∞(Ω). Moreover, if there exist  k>0 and  v¯>0 such that   infv>v¯vkγ(v)>0,then the global solution is bounded uniformly in time.}
}