论文标题
具有非局部分散和异质环境的逻辑模型中总人口的优化
Optimisation of total population in logistic model with nonlocal dispersals and heterogeneous environments
论文作者
论文摘要
在本文中，我们调查了根据资源分布M（x）和扩散率D最大化总均衡人群在规定的总资源中，在具有非局部分散的物流模型中。除其他外，我们表明，对于$ d \ ge1 $，存在$ c_0，c_1> 0 $，具体取决于$ \ | | m \ | _ {l^1} $，因此$ c_0 \ sqrt {d} <\ mbox {扩散是NI提出的猜想，并在[3]中证明是合理的，表明在一维情况下，总人口的至上$ = 3 \ | m \ | _ | _ {l^1} $。这反映了具有本地和非局部分散策略的模型之间的严重差异。
In this paper, we investigate the issue of maximizing the total equilibrium population with respect to resources distribution m(x) and diffusion rates d under the prescribed total amount of resources in a logistic model with nonlocal dispersals. Among other things, we show that for $d\ge1$, there exist $C_0, C_1>0$, depending on the $\|m\|_{L^1}$ only, such that $$C_0\sqrt{d}<\mbox{supremum~ of~ total~ population}<C_1\sqrt{d}.$$ However, when replaced by random diffusion, a conjecture, proposed by Ni and justified in [3], indicates that in the one-dimensional case, supremum of total population$=3\|m\|_{L^1}$. This reflects serious discrepancies between models with local and nonlocal dispersal strategies.
