中文摘要：

本文考虑了一类具有比率依赖的食物链模型,目前对这个扩散模型已经讨论得到的结果非常少.本文首先讨论了该弱耦合扩散模型平衡解的存在性、一致有界性和稳定性.接着,证明了含交错扩散项的偏微模型在空间维数小于或等于6时的经典解的存在性.

英文摘要：

In this article,a ratio-dependent food chain model is studied.Very few mathematical results are known for this model with diffusion.First,the existence and uniform boundedness of global solutions and stability of the equilibrium points for the model of weakly coupled reaction-diffusion type are discussed.Then,we prove the existence of global classical solutions for the model of PDE type with cross-diffusion when the space dimension n6.