论文标题
非线性年龄和两性种群动态结构模型的无效可控性
Null controllability of a nonlinear age and two-sex population dynamics structured model
论文作者
论文摘要
本文致力于研究非线性年龄和两性种群动力学结构模型的无效可控性能，而无需空间结构。在这里，非线性和耦合处于出生水平。 \ noindent在这项工作中，我们考虑了两个无效可控性问题的情况。 \ noindent第一个问题与男性和女性亚群密度的灭绝有关。 \ noindent第二种情况涉及男性或女性亚群体的无效可控性。在这两种情况下，如果$ a $都是最大年龄的预期寿命，则在男性或女性灭绝后持续时间$ a $的时间间隔，就必须获得人口的总灭绝。 \ noIndent我们的方法首先使用与辅助系统的伴随，线性辅助系统的无可控性以及Kakutani的固定点定理之后的可观察性不等式。
This paper is devoted to study the null controllability properties of a nonlinear age and two-sex population dynamics structured model without spatial structure. Here, the nonlinearity and the couplage are at birth level. \noindent In this work we consider two cases of null controllability problem. \noindent The first problem is related to the extinction of male and female subpopulation density. \noindent The second case concerns the null controllability of male or female subpopulation individuals. In both cases, if $A$ is the maximal age expectancy, a time interval of duration $A$ after the extinction of males or females, one must get the total extinction of the population. \noindent Our method uses first an observability inequality related to the adjoint of an auxiliary system, a null controllability of the linear auxiliary system and after the Kakutani's fixed point theorem.
