含移流项两物种竞争模型关于资源的最优控制  

Optimal Control of Resource in Two Competing Species Model with Advection Terms

作　　者：梁浩健 李辉来[1] LIANG Haojian;LI Huilai(College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2019年第3期500-504,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11271154)

摘　　要：用含移流项的反应扩散方程描述两物种竞争模型,期望对资源进行分配时,使生态系统中整个时间段内两物种的加权密度和最终时刻的加权密度达到最大值.通过对方程解的存在性、最优控制的存在性及最优控制问题必要性条件的证明,表明当资源分配满足bang-bang控制时,种群密度达到最大值.We described two competing species model by a reaction-diffusion equation with advection term. We hoped that when resources were allocated, the weighted density of two species in the ecosystem reached the maximum during the whole time period and at the final time. By proving the existence of the solution of the equation, the existence of an optimal control and the necessary condition of the optimal control problem, and the results show that the population density reaches the maximum when the resource allocation satisfies a bang-bang control.

关 键 词：反应扩散移流方程 最优控制 种群模型 伴随方程 

分 类 号：O232[理学—运筹学与控制论]