非线性捕食-被捕食反应扩散系统的奇摄动

非线性捕食-被捕食反应扩散系统的奇摄动 Singular Perturbation of Nonlinear Predator-Prey Reaction Diffusion Systems 姚静荪 YAO Jing-sun 1 2 first-author 莫嘉琪 MO Jia-qi 1 2 安徽师范大学数学系 安徽师范大学数学系 Department of Mathematics, Anhui Normal University Department of Mathematics, Anhui Normal University 安徽师范大学数学系,安徽,芜湖,241000 安徽师范大学数学系,安徽,芜湖,241000 在适当的条件下,利用微分不等式理论,讨论了一个初始边值问题解的存在性和渐近性态.微分不等式理论的实质是构造两个辅助函数作为系统的上、下解.本文是利用微分不等式方法来研究一类生物数学中的非线性奇摄动捕食-被捕食反应扩散系统.然后使上、下解分别满足相应的不等式.最后证明所研究的系统存在解并处在上、下解之间.从而证明了系统解的存在性,并同时得到解的估计. The existence and asymptotic behavior of solution for the initial boundary value problems are studied by using the theory of differential inequalities. The theory of differential inequalities is really to constructing two auxiliary functions, which are super and lower solutions of the system respectively. In this paper, a class of system for nonlinear reaction diffusion of the predator-prey in the biomathematics is considered using the method of differential inequalities. And then the super and lower solutions are satisfied corresponding inequalities. Finally, there is a solution of the system between the super solution and lower solution. Then the existence of the solution for the system is proved and the asymptotic estimation is obtained. 非线性 捕食-被捕食 反应扩散 奇摄动 nonlinear predator-prey reaction diffusion singular perturbation O175.29 国家自然科学基金资助项目（90111011,10471039）;浙江省自然科学基金资助项目（Y60417） 2005-03-01 2021-04-01 3