中文摘要：

本文应用Sobolev嵌入定理和bootstrap技巧证明竞争-竞争-互惠交错扩散模型在空间维数小于10时古典解的整体存在唯一性。

英文摘要：

Using Sobolev embedding theorems and bootstrap arguments,the existence and uniqueness of nonnegative global existence of classical solutions for the competitor-competitor-mutualist model with cross-diffusion are proved when the space dimensions is less than 10.