一类具有内部存储和外部抑制剂的恒化器模型  

A system of reaction-diffusion equations in the chemostat with internal storage and external inhibitor

作　　者：李双妃 王艳娥[2] LI Shuangfei;WANG Yan′e(School of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710119,China;School of Computer Science,Shaanxi Normal University,Xi′an 710119,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119 [2]陕西师范大学计算机科学学院,陕西西安710119

出　　处：《纺织高校基础科学学报》2018年第3期348-355,共8页Basic Sciences Journal of Textile Universities

基　　金：陕西省自然科学基础研究计划项目(2014JM1003)

摘　　要：为研究内部存储和外部抑制剂对物种存活/死亡的影响,提出一类具有内部存储和外部抑制剂的非均匀恒化器模型.考虑模型的适定性问题,得到模型古典解的存在唯一性.借助于一个非线性特征值问题主特征值的符号判断物种的存活/死亡.运用单调动力学系统理论证明了物种存活时正平衡解的唯一性以及全局吸引性.To study the impact of internal storage external inhibitor on the persistence/extinction of single species, a system of reaction-diffusion equations in the unstirred chemostat with internal storage and external inhibitor is proposed.The existence and uniqueness of the classical solution of the model are obtained by considering the well-posedness of the model. The persistence/extinction of single species is determined by the sign of the principal eigenvalue of a nonlinear eigenvalue problem.The uniqueness and global attractivity of the positive steady state are proved when the species persists by the theory of monotone dynamics.

关 键 词：恒化器 内部存储 外部抑制剂 非线性特征值问题 比较原理 

分 类 号：O175.26[理学—数学]