In this paper, we consider an age-structured population model with diffusion. We first establish a comparison principle. We then apply the comparison principle to show the existence and uniqueness of solutions by constructing monotone sequences of weak upper and lower solutions. We also use the comparison principle to study the long-time behavior of the solution and present extinction and boundedness results under certain conditions on the parameters in the model. Additionally, as an example of its application, we apply the model to describe the dynamics of a forest population.

中文翻译：

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年龄和空间相关种群模型的分析：在森林生长中的应用

在本文中，我们考虑具有扩散的年龄结构人口模型。我们首先建立一个比较原理。然后，我们通过构造弱上下解的单调序列，应用比较原理来显示解的存在性和唯一性。我们还使用比较原理研究了溶液的长期行为，并在一定条件下对模型中的参数给出了灭绝和有界结果。另外，作为其应用的示例，我们将模型应用于描述森林种群的动态。