"In this paper we consider a two-sex population model proposed by Hoppenstead. We do not assume any special form of the mating function. We address the problem of existence and uniqueness of continuous and classical solutions. We give sufficient conditions for continuous solutions to exist globally and we show that they have in fact a directional derivative in the direction of the characteristic lines and satisfy the equations of the model with the directional derivative replacing the partial derivatives. The existence of classical solutions is established with mild assumptions on the vital rates." (EXCERPT)

中文翻译：

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两性年龄结构人口模型：良好姿势

“在本文中，我们考虑了 Hoppenstead 提出的两性种群模型。我们不假设任何特殊形式的交配函数。我们解决了连续解和经典解的存在性和唯一性问题。我们给出了连续解的充分条件全局存在，我们证明它们实际上在特征线的方向上有一个方向导数，并且满足模型的方程，其中方向导数代替偏导数。经典解的存在是在生命率的温和假设下建立的.” （摘抄）