n个种群趋趋化模型解的整体存在性（英文）

GLOBAL BOUNDEDNESS IN A N-SPECIES CHEMOTAXIS SYSTEM

本论文研究了如下的趋化模型在Ω■R^N(N≥1)中整体解的存在性。其中参数满足a_(ii)>0,d_i>0,μ_i>0,X_i>0,k_i>0,a_(ij)≥0,λ>0 for i,j=1,…,n.令q_i=χ_i/(μ_ia_(ii)).通过运用M矩阵的一些性质得到结论如下:若矩阵■满足ρ(B)<1,那么上面的趋化模型存在唯一的整体解.其中ρ(B)为矩阵B的谱半径.

In this paper we consider the following system involving more than two competitive populations of biological species all of which are attracted by the same chemoattractant{u1t=d1△u1-x1 ·（u1 w）＋μ1u1（1-∑n i=1 a1iui）,x∈Ω,t〉0,u2t=d2△u2-x2 ·（u2 w）＋μ2u2（1-∑n i=1 a2iui）,x∈Ω,t〉0,unt=dn△un-xn ·（un1 w）＋μnun（1-∑n i=1 aniui）,x∈Ω,t〉0,-△w＋λw=∑kiui,x∈Ω,t〉0 under homogeneous Neummann boundary conditions in a bounded domain Ω∈ R^N（N≥1）with smooth boundary and aii 0,di〉0,〉μi〉0,xi〉0,ki〉0,aij≥0,λ〉0 for i ,j=1,...,n.Denote by qi=xi/μiaii.We proved that if the matrix {B=（k1q1 k2q1…knqi k2q2 k2q2…knq2） （k1qn k2qn…knqn} satisfies that in which the p（B） is the spectral radius of B, then the solution to the system above is unique and globally bounded by applying the properties of the M-matrix.