具有Dirichlet边界条件的logistic方程的物种总质量与资源的比值

IF 1 3区数学 Q1 MATHEMATICS

Communications on Pure and Applied Analysis Pub Date : 2022-06-09 DOI:10.3934/cpaa.2023009

Jumpei Inoue

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引用次数: 0

摘要

我们考虑了具有齐次Dirichlet边界条件的扩散逻辑方程的平稳问题。关于相应的诺依曼问题，倪伟明提出了一个问题：最大化物种总量与资源的比例。对于这个问题，白、何和李证明了在一维情况下该比值的上确界为3，作者和库托证明了在多维球中该上确界是无穷大。在本文中，我们证明了同样的结果仍然适用于狄利克雷问题。我们的证明是基于次超解方法，并且由于解存在的扩散率的范围，需要更精细的计算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the ratio of total masses of species to resources for a logistic equation with Dirichlet boundary condition

We consider the stationary problem for a diffusive logistic equation with the homogeneous Dirichlet boundary condition. Concerning the corresponding Neumann problem, Wei-Ming Ni proposed a question as follows: Maximizing the ratio of the total masses of species to resources. For this question, Bai, He and Li showed that the supremum of the ratio is 3 in the one dimensional case, and the author and Kuto showed that the supremum is infinity in the multi-dimensional ball. In this paper, we show the same results still hold true for the Dirichlet problem. Our proof is based on the sub-super solution method and needs more delicate calculation because of the range of the diffusion rate for the existence of the solution.

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来源期刊

Communications on Pure and Applied Analysis 数学-数学

CiteScore

1.90

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. Invited expository articles are also published from time to time. It is edited by a group of energetic leaders to guarantee the journal''s highest standard and closest link to the scientific communities.