In this paper we study the null controllability property for a single population model in which the population y depends on time t, space x, age a and size \(\tau \). Moreover, the diffusion coefficient k is degenerate at a point of the domain or both extremal points. Our technique is essentially based on Carleman estimates. The \(\tau \) dependence requires us to modify the weight for the Carleman estimates, and accordingly the proof of the observability inequality. Thanks to this observability inequality we obtain a null controllability result for an intermediate problem and finally for the initial system through suitable cut off functions.

在本文中，我们研究了单个种群模型的零可控性，其中种群y取决于时间t、空间x、年龄a和大小\(\tau \)。此外，扩散系数k在域的一个点或两个极值点退化。我们的技术基本上是基于 Carleman 估计的。该\（\ tau蛋白\）的依赖，需要我们修改的重量为估计的Carleman，并相应地可观测不等式的证明。由于这种可观察性不等式，我们通过合适的截断函数获得了中间问题和最终初始系统的零可控性结果。