摘要
研究一类周期环境中具有尺度结构的线性害鼠模型的适定性及最优不育控制问题.首先应用积分方程及算子谱半径理论证明模型解的存在唯一性以及模型解关于控制变量的连续依赖性等有关性质,接着利用极小化序列和Mazur定理确立最优不育控制策略的存在性,最后借助非线性分析中的切锥-法锥技巧导出最优不育控制策略的结构.
In this paper,well-posedness and optimal contraception control of size-structured population model in periodic environments are investigated. Firstly, by ues of Volterra integral equation and spectral radius of linear operator,we have proven the existence and uniqueness of solution to the model. Secondly we prove the existence of optimal contraception policies via a minimizing sequence and a use of Mazur＇s theorem in convex analysis. Following that is a careful derivation of necessary optimality conditions, which is finished by tangent- normal cones and adjoint techniques.
出处
《数学的实践与认识》
北大核心
2016年第6期193-203,共11页
Mathematics in Practice and Theory
基金
国家自然科学基金(11371313)
吕梁学院校内基金(ZFXN201512)
关键词
周期环境
尺度结构
不育控制
谱理论
共轭系统
periodic environment
size-structured
contraception control
spectral radius adjoint system
