物种生存资源的最优控制
Optimal control of resources for species survival
摘要：
考虑一个物种，其种群密度在非均匀环境中求解稳态扩散Logistic方程，该非均匀环境借助于代表给定盒子中资源分布的空间非常数系数来建模。我们研究在生物学相关的约束条件下，最大化总总体规模与资源分配的关系。在物种扩散率足够大的条件下，证明了任何一种最优配置都是代表资源区位的区域的特征函数。此外，我们强调，最佳配置看{ \it集中}时，扩散率是足够大的。在一维的情况下，这个问题进行了深入的分析，并为大的扩散率，所有的最佳配置。
英文摘要：
Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We look at maximizing the total population size with respect to resources distribution, under some biologically relevant constraints. Assuming that the diffusion rate of the species is large enough, we prove that any optimal configuration is the characteristic function of a domain standing for the resources location. Moreover, we highlight that optimal configurations look {\it concentrated} whenever the diffusion rate is large enough. In the one-dimensional case, this problem is deeply analyzed, and for large diffusion rates, all optimal configurations are exhibited.
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