THE EIGENVALUE PROBLEM OF SOME NONLOCAL DIFFUSION SYSTEMS

一些非局部扩散系统的特征值问题

张婷

11930001

硕士

数学

苏琳琳

2021-05-22

2021-05-22

南方科技大学

深圳

In this paper, we investigate the eigenvalue problem of some systems of nonlocaldiffusion models. We characterize the principal eigenvalue 𝜆𝑝 of the system in a max­minfashion. Then we show that 𝜆𝑝 has a corresponding positive eigenvector, its algebraicmultiplicity is 1, and it is isolated.For the eigenvalue problem of systems of local operators, such as the second orderelliptic operators, similar results were obtained by the Krein­Rutman theorem in literatures. But for the systems of nonlocal operators studied in this paper, the Krein­Rutmantheorem fails. I use an elementary and complex method to prove the results.

本文考虑了一些非局部扩散系统的特征值问题。在该文中我们证明了这些非局部扩散系统的主特征值能用“max­min”形式刻画。主特征值所对应的特征向量是正向量，我们证明了它的代数重数是 1，而且它是孤立的。对于局部系统的特征值问题，例如二阶椭圆算子，有些文献用 Krein­Rutman定理得到了类似的结果。但对于我考虑的这些非局部扩散系统，Krein­Rutman 定理的条件不满足，所以我用了一个复杂的初等方法来证明。

nonlocal diffusion systems principal eigenvalue max­min characterization

非局部扩散系统 主特征值 max­min 刻画

英语

独立培养

南方科技大学

Zhang T. THE EIGENVALUE PROBLEM OF SOME NONLOCAL DIFFUSION SYSTEMS[D]. 深圳. 南方科技大学,2021.