Maximal total population of species in a diffusive logistic model
Maximal total population of species in a diffusive logistic model
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DOI：
10.1007/s00285-022-01817-0
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发表时间：
2022-10
影响因子：
1.9
通讯作者：
C. Kao;S. Mohammadi
中科院分区：
文献类型：
--
作者：
C. Kao;S. Mohammadi
本文研究了一类具有固定资源的定态扩散Logistic方程所支配的单种群的最大化问题。对于大的扩散率，将讨论对称性等最大化者的定性性质。我们的研究结果是符合以前的研究结果，断言大扩散，集中的资源有利于最大限度地提高总人口。然后，基于重排理论导出了最大化的最优性条件。我们开发了一个有效的数值算法，适用于不同的几何形状的域，以计算最大化。证明了该算法是收敛的。我们的数值模拟给出了一个真实的洞察的定性性质的最大化，也导致我们对最大化的一些解释。
In this paper, we investigate the maximization of the total population of a single species which is governed by a stationary diffusive logistic equation with a fixed amount of resources. For large diffusivity, qualitative properties of the maximizers like symmetry will be addressed. Our results are in line with previous findings which assert that for large diffusion, concentrated resources are favorable for maximizing the total population. Then, an optimality condition for the maximizer is derived based upon rearrangement theory. We develop an efficient numerical algorithm applicable to domains with different geometries in order to compute the maximizer. It is established that the algorithm is convergent. Our numerical simulations give a real insight into the qualitative properties of the maximizer and also lead us to some conjectures about the maximizer.