On Principal Spectrum Points/Principal Eigenvalues of Nonlocal Dispersal Operators and Applications

By Wenxian Shen, Xiaoxia Xie. 2013

53 citations recorded by the source corpus.

This paper is to investigate the dependence of the principal spectrum points of nonlocal dispersal operators on underlying parameters and to consider its applications. In particular, we study the effects of the spatial inhomogeneity, the dispersal rate, and the dispersal distance on the existence of the principal eigenvalues, the magnitude of the principal spectrum points, and the asymptotic behavior of the principal spectrum points of nonlocal dispersal operators with Dirichlet type, Neumann type, and periodic boundary conditions in a unified way. We also discuss the applications of the principal spectral theory of nonlocal dispersal operators to the asymptotic dynamics of two species competition systems with nonlocal dispersal.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/81e154c7ae7b0514e1e93a3773ecd2ec7f90744d

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

On eigenvalue problems arising from nonlocal diffusion models (2016, unknown): “Shen and Xie [18] considered the special case κ(x, y) = κ(y−x) and proved that if max Ω̄ a(x)−min Ω̄ a(x) inf x∈Ω̄ ∫ Ω κ(y − x)dy, then a positive and continuous eigenfunction exists.”
On the definition and the properties of the principal eigenvalue of some nonlocal operators (2015, methodology): “If the behaviour of λp(LΩ + a) with respect to a or Ω can be exhibited directly from the definition, the impact of scalings of the kernel is usually unknown and has been largely ignored in the literature except in some specific situations involving particular nonlocal dispersal operators defined in ”