In this paper, we consider a cascaded taxis model for two proliferating and degrading species which thrive on the same nutrient but orient their movement according to different schemes. In particular, we assume the first group, the foragers, to orient their movement directly along an increasing gradient of the food density, while the second group, the exploiters, instead track higher densities of the forager group. Specifically, we will investigate an initial boundary-value problem for a prototypical forager–exploiter model of the form [Formula: see text] in a smoothly bounded domain [Formula: see text], where [Formula: see text], [Formula: see text] is nonnegative and the functions [Formula: see text] are assumed to satisfy [Formula: see text], [Formula: see text] as well as [Formula: see text] respectively, with constants [Formula: see text], [Formula: see text] and [Formula: see text] and [Formula: see text].Assuming that [Formula: see text], [Formula: see text] and that [Formula: see text] satisfies certain structural conditions, we establish the global solvability of this system with respect to a suitable generalized solution concept and then, for the more restrictive case of [Formula: see text] and [Formula: see text], investigate an eventual regularity effect driven by the decay of the nutrient density [Formula: see text].

中文翻译：

---

具有超线性退化及其最终规律性的觅食者-剥削者模型的全局广义解

在本文中，我们考虑了两个增殖和降解物种的级联出租车模型，这些物种在相同的养分上茁壮成长，但根据不同的方案定位它们的运动。特别是，我们假设第一组，觅食者，直接沿着食物密度的增加梯度定向他们的运动，而第二组，剥削者，则跟踪觅食者群体的更高密度。具体来说，我们将研究在平滑有界域 [Formula: see text] 中 [Formula: see text] 形式的原型 forager-exploiter 模型的初始边值问题，其中 [Formula: see text], [Formula: see text] 是非负的，假设函数 [Formula: see text] 分别满足 [Formula: see text]、[Formula: see text] 和 [Formula: see text]，并带有常数 [Formula: see text] ,