一类多物种生物趋化模型解的局部性质

LOCAL PROPERTY OF SOLUTIONS TO A MULTI-SPECIES CHEMOTAXIS SYSTEM

本文主要研究一类多物种生物趋化模型在齐次Neumann初边值条件下,证得方程组的解的局部存在性及唯一性。即在光滑且有界边界Ω?n(n≥1),当初值(u10(x),…,uN0(x))∈(C0(Ω))N,w0∈W1,r(Ω)非负,利用Banach空间不动点定理证明解的局部存在性,再利用Gronwall不等式和能量方法证得解的唯一性。

This dissertation is devoted to study the local existence and uniqueness of solutions to a chemotaxis muti-speies system with logistic source, under homogeneous Neumann boundary conditions Ω? n . If the nonnegative initial data ( u 10 (x),…,u N0 (x))∈(C 0(Ω)) N and w 0∈W 1,r (Ω), By the Banach fixed point theorem, we establish the local existence of the solution. By the Gronwall inequality and energy method, we also prove the uniqueness of the local solution.