Approximations of random dispersal operators/equations by nonlocal dispersal operators/equations

DOI10.1016/j.jde.2015.08.026zbMath1328.35069arXiv1402.6353OpenAlexW1789529154MaRDI QIDQ499540

Wenxian Shen, Xiaoxia Xie

Publication date: 30 September 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.6353

zbMATH Keywords

principal eigenvalueKPP equationnonlocal dispersalrandom dispersalprincipal spectrum pointpositive time periodic solution

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) Population dynamics (general) (92D25) Theoretical approximation in context of PDEs (35A35) Eigenvalue problems for integral equations (45C05) Integro-partial differential equations (35R09)

Related Items (31)

Approximation of random diffusion equations by nonlocal diffusion equations in free boundary problems of one space dimension ⋮ Local approximation of heterogeneous porous medium equation by some nonlocal dispersal problems ⋮ The dynamics of partially degenerate nonlocal diffusion systems with free boundaries ⋮ Limiting solutions of nonlocal dispersal problem in inhomogeneous media ⋮ Sparse Monte Carlo Method for Nonlocal Diffusion Problems ⋮ Nonlocal dispersal equations in time-periodic media: principal spectral theory, limiting properties and long-time dynamics ⋮ Propagation and reaction–diffusion models with free boundaries ⋮ The generalised principal eigenvalue of time-periodic nonlocal dispersal operators and applications ⋮ The spectral bound and basic reproduction ratio for nonlocal dispersal cooperative problems ⋮ Perturbation problem for the indefinite nonlocal periodic-parabolic equation ⋮ Criteria for the existence and lower bounds of principal eigenvalues of time periodic nonlocal dispersal operators and applications ⋮ Threshold dynamics of a time-periodic nonlocal dispersal SIS epidemic model with Neumann boundary conditions ⋮ Principal spectral theory of time‐periodic nonlocal dispersal operators of Neumann type ⋮ Non-local dispersal equations with almost periodic dependence. II: Asymptotic dynamics of Fisher-KPP equations ⋮ Principal spectral theory for nonlocal systems and applications to stem cell regeneration models ⋮ Approximation solutions of some nonlocal dispersal problems ⋮ Principal spectral theory in multigroup age-structured models with nonlocal diffusion ⋮ Criteria for the existence of principal eigenvalues of time periodic cooperative linear systems with nonlocal dispersal ⋮ Propagation, diffusion and free boundaries ⋮ On principal spectrum points/principal eigenvalues of nonlocal dispersal operators and applications ⋮ Asymptotic behaviors for nonlocal diffusion equations about the dispersal spread ⋮ Spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions and applications ⋮ Coexistence and extinction in time-periodic Volterra-Lotka type systems with nonlocal dispersal ⋮ Approximation of random diffusion by nonlocal diffusion in age-structured models ⋮ Dynamics of a nonlocal diffusive logistic model with free boundaries in time periodic environment ⋮ Nonlocal dispersal equations with almost periodic dependence. I. Principal spectral theory ⋮ The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries ⋮ Global asymptotic stability of constant equilibrium in a nonlocal diffusion competition model with free boundaries ⋮ Nonlocal dispersal equations in domains becoming unbounded ⋮ Free boundary problems for the local-nonlocal diffusive model with different moving parameters ⋮ Effects of boundary and spatial heterogeneity on nonlocal dispersal equations

Cites Work

• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Effects of spatial variations and dispersal strategies on principal eigenvalues of dispersal operators and spreading speeds of monostable equations
• Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity
• Spreading speeds and traveling waves of nonlocal monostable equations in time and space periodic habitats
• On principal spectrum points/principal eigenvalues of nonlocal dispersal operators and applications
• On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators
• The principal eigenvalue of a space-time periodic parabolic operator
• Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions
• Spectral theory for general nonautonomous/random dispersal evolution operators
• Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal
• Non-local dispersal.
• Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats
• Entire solutions in the Fisher-KPP equation with nonlocal dispersal
• Existence and uniqueness of the solution of a space-time periodic reaction-diffusion equation
• Spectral theory for nonlocal dispersal with periodic or almost-periodic time dependence
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• Convergence to spatial-temporal clines in the Fisher equation with time-periodic fitnesses
• Multidimensional nonlinear diffusion arising in population genetics
• Propagation speed of travelling fronts in non local reaction-diffusion equations
• The evolution of dispersal
• Domain perturbation for linear and nonlinear parabolic equations
• Criteria for the existence and lower bounds of principal eigenvalues of time periodic nonlocal dispersal operators and applications
• Global dynamics of a competition model with non-local dispersal. I: The shadow system
• Random dispersal vs. non-local dispersal
• How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
• Asymptotic behavior for nonlocal diffusion equations
• Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations
• Evolutionary stability of ideal free nonlocal dispersal
• Uniform convergence for elliptic problems on varying domains
• Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity
• Spatial Ecology via Reaction‐Diffusion Equations
• Global attractivity and stability in some monotone discrete dynamical systems
• RANDOM DISPERSAL IN THEORETICAL POPULATIONS
• Dynamical systems in population biology

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