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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2020, Vol. 37 ›› Issue (4): 442-458.doi: 10.3969/j.issn.1005-3085.2020.04.005

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一类具有内部存储和外部抑制剂的非均匀恒化器模型

李双妃,   王治国,   曹   毅   

  1. 陕西师范大学数学与信息科学学院，西安  710119
  • 收稿日期:2018-05-09 接受日期:2019-06-11 出版日期:2020-08-15 发布日期:2020-10-15
  • 通讯作者: 王治国 E-mail: zgwang@snnu.edu.cn
  • 基金资助:
    国家自然科学基金(61672021)；陕西省自然科学基础研究计划(2014JM1003).

A System of Reaction-diffusion Equations in the Unstirred Chemostat with Internal Storage and External Inhibitor

LI Shuang-fei,   WANG Zhi-guo,   CAO Yi   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119
  • Received:2018-05-09 Accepted:2019-06-11 Online:2020-08-15 Published:2020-10-15
  • Contact: Z. Wang. E-mail address: zgwang@snnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (61672021); the Natural Science Basic Research Plan in Shaanxi Province (2014JM1003).

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摘要： 本文讨论了一类具有内部存储和外部抑制剂的非均匀恒化器模型．首先，为克服比率奇性，利用最大值原理建立关于模型更精确的先验估计，进而构造比通常正锥更小的特殊锥．其次，借助单调方法和特殊锥上的度理论，研究模型共存解存在的充分条件．结果表明，当相应的非线性特征值问题的主特征值同正或同负时，系统至少存在一个正解．

关键词: 恒化器, 内部存储, 外部抑制剂, 单调方法, 不动点理论

Abstract: A system of reaction-diffusion equations in the unstirred chemostat with internal storage and external inhibitor is considered in this paper. Firstly, in order to overcome the ratio singularity, the sharp priori estimates for positive solutions of the system are established by the maximum principle, and then a special cone smaller than the usual positive cone is constructed. Secondly, the sufficient conditions for the existence of the model coexistence solution are studied by the monotone method and the topological degree theory on the special cone. It turns out that there exists at least one positive solution when the principal eigenvalues of the corresponding nonlinear eigenvalue problems are both positive or negative.

Key words: chemostat, internal storage, external inhibitor, monotone method, fixed point theory

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