论文标题
非线性年龄，空间和两性结构种群动力学模型的无效可控性
Null Controllability of a nonlinear age, space and two-sex structured population dynamics model
论文作者
论文摘要
在本文中，我们研究了非线性年龄，空间和两性结构种群动力学模型的无效可控性。该模型使得非线性和耦合处于出生水平。 我们考虑一个有男性和女性的人群，我们正在处理两个无效可控性问题的案例。第一个问题与总灭绝有关，这意味着，我们估计将男性和女性亚群密度提高到零的时间$ t $。第二种情况是涉及男性或女性亚群体的无效可控性。在这里，如果$ a $是个人的寿命，那么当时$ t+a $一个人将获得人口的总灭绝。 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Schauder的固定点定理相关的可观察性不平等。
In this paper, we study the null controllability of a nonlinear age, space and two-sex structured population dynamics model. This model is such that the nonlinearity and the couplage are at birth level. We consider a population with males and females and we are dealing with two cases of null controllability problem. The first problem is related to the total extinction, which means that, we estimate a time $T$ to bring the male and female subpopulation density to zero. The second case concerns null controllability of male or female subpopulation individuals. Here, So if $A$ is the life span of the individuals, at time $T+A$ one will get the total extinction of the population. 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 Schauder's fixed point theorem.
