关于扩散Logistic方程物种资源比的无界性
On the unboundedness of the ratio of species and resources for the diffusive logistic equation
摘要：
关于一类扩散Logistic方程，Ni [1，摘要]提出了一个考虑物种和资源的L^1范数之比的上确界的最优化问题，通过改变扩散速率和资源的分布，并给出了一维情形下上确界为3的猜想.在[1]中，白，何和李证明了这个猜想的有效性。本文证明了当栖息地是一个多维球时，上确界是无穷大的。我们的证明是基于次上解方法。证明的一个关键思想是构造一个L^1无界的子解序列。
英文摘要：
Concerning a class of diffusive logistic equations, Ni [1, Abstract] proposed an optimization problem to consider the supremum of the ratio of the L^1 norms of species and resources by varying the diffusion rates and the profiles of resources, and moreover, he gave a conjecture that the supremum is 3 in the one-dimensional case. In [1], Bai, He and Li proved the validity of this conjecture. The present paper shows that the supremum is infinity in a case when the habitat is a multi-dimensional ball. Our proof is based on the sub-super solution method. A key idea of the proof is to construct an L^1 unbounded sequence of sub-solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
