带非线性扩散项和信号产生项的趋化-趋触模型解的整体有界性  

Global Boundedness in a Chemotaxis-Haptotaxis Model with Nonlinear Diffusion and Signal Production

作　　者：贾哲 杨作东[2,3] Jia Zhe;Yang Zuodong(School of Mathematics and Statistics,Linyi University,Shandong Linyi 276005;School of Teacher Education,Nanjing Normal University,Nanjing 210097;School of Teacher Education,Nanjing University of Information Science and Technology,Nanjing 210044)

机构地区：[1]临沂大学数学与统计学院,山东临沂276005 [2]南京师范大学教师教育学院,南京210097 [3]南京信息工程大学教师教育学院,南京210044

出　　处：《数学物理学报（A辑）》2021年第5期1382-1395,共14页Acta Mathematica Scientia

基　　金：国家自然科学基金(11571093);江苏省教育委员会自然科学基金(19KJB110016);临沂大学科研启动基金(LYDX2020BS014)。

摘　　要：该文研究如下带齐次Neumann边界条件的趋化一趋触模型的初边值问题{ut=∇⋅(D(u)∇u)−χ∇⋅(u(1+u)α∇v)−ξ∇⋅(u(1+u)β∇w)+u(a−μuk−1−λw),vt=△v−v+uγ,x∈Ω,t>0,wt=−vw,x∈Ω,t>0,其中Ω■R3为有界域,χ,ξ,μ,λ,γ>0,k>1,a∈R,且D(u)≥CD(u+1)m-1,其中CD>0,m∈R.主要结论如下(i)当0<γ≤2/3时,若α>γ-k+1并且β>1-k,上述模型存在整体有界的古典解.(ii)当2/3<γ≤1时,若α>γ-k+1/e+1并且■,或者α>γ-k+1并且■,上述模型存在整体有界的古典解.This paper is concerned with an initial-boundary value problem for the following chemotaxis-haptotaxis model{ut=∇⋅(D(u)∇u)−χ∇⋅(u(1+u)α∇v)−ξ∇⋅(u(1+u)β∇w)+u(a−μuk−1−λw),vt=△v−v+uγ,x∈Ω,t>0,wt=−vw,x∈Ω,t>0,under homogenous Neumann boundary condition in a bounded domainΩ⊂R^(3),withχ,ξ,μ,λ,γ>0,k>1,a∈R,and D(u)≥CD(u+1)m−1 for CD>0,m∈R.It is shown that(i)For 0<γ≤23,ifα>γ−k+1 andβ>1−k,there is a classical solution(u,v,w)which is globally bounded to the above problem.(ii)For 23<γ≤1,ifα>γ−k+1e+1 andβ>max{(3γ−2)(3γ+2k−2)6−k+1,(3γ−2)(γ+1e)3−k+1},orα>γ−k+1 andβ>max{(3γ−2)(3γ+2k−2)6−k+1,(3γ−2)(α+k−1)3−k+1},there is a classical solution(u,v,w)which is globally bounded to the above problem.

关 键 词：整体存在性 有界性 趋化-趋触 非线性扩散 

分 类 号：O175.26[理学—数学]