带比例功能反应函数食物链交错扩散模型的整体解
GLOBAL SOLUTIONS FOR THE RATIO-DEPENDENT FOOD-CHAIN MODEL WITH CROSS-DIFFUSION

本文研究了带有比例功能反应函数食物链交错扩散模型整体解的存在性和正平衡点的稳定性.利用能量方法和Gagliardo-Nirenberg型不等式,获得了该模型整体解的存在性和一致有界性,同时通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件.
In this paper, a food chain model with ratio-dependent functional response is investigated under homogeneous Neumann boundary conditions. Using the energy estimate and Gagliardo-Nirenberg-type inequalities, the existence and the uniform boundedness of global solutions are proved. Meanwhile, the sufficient condition for global asymptotic stability of the positive equilibrium point for the model is given by constructing the Lyapunov function