Asymptotic speeds of spread for a nonlocal diffusion equation
type: Item
instance of: scholarly article
title: Asymptotic speeds of spread for a nonlocal diffusion equation
zbMATH Open document ID: 1397.35139
author: Zhaoquan Xu
published in: Journal of Dynamics and Differential Equations
publication date: 2018-08-21T00:00:00Z
review text: The author studies the spatial spreading dynamics of a class of nonlocal diffusion equation \[ {u_t}(t,x) = (J * u - u)(t,x) + f(u,G * * S(u))(t,x), \] where \(t \geq 0\), \(x \in \mathbb R\) and \(J \in {L^1}(\mathbb R)\) is a nonnegative symmetric kernel function. In a former work for the same equation, the author proved that there exists a critical speed \({c^ * } > 0\) such that this nonlocal diffusion equation has a unique regular traveling wave solution if and only if \(c > {c^ * }\) in the case when the investigated equation does not necessarily admit the comparison principle. The present paper establishes that this \({c^ * }\) is the asymptotic speed of propagation. In additional as an application of the obtained theoretical results, are considered some models which arising from population dynamics and neural network and the corresponding spreading speed are established for these models.
reviewed by: Andrey Zahariev
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6921336
zbMATH Keywords: spreading speeds
zbMATH Keywords: nonlocal diffusion
zbMATH Keywords: spatio-temporal delays
MaRDI profile type: Publication
full work available at URL: s10884-016-9555-1
OpenAlex ID: W2526965322
Wikidata QID: Q115383486
cites work: Q4134311
cites work: Q4089232
cites work: Multidimensional nonlinear diffusion arising in population genetics
cites work: Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal
cites work: Traveling waves in a convolution model for phase transitions
cites work: Spatial Structures and Periodic Travelling Waves in an Integro-Differential Reaction-Diffusion Population Model
cites work: Traveling fronts for a class of non-local convolution differential equations
cites work: Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations
cites work: Uniqueness of travelling waves for nonlocal monostable equations
cites work: On a non-local equation arising in population dynamics
cites work: Run for your life. A note on the asymptotic speed of propagation of an epidemic
cites work: Spatial dynamics of a nonlocal and time-delayed reaction-diffusion system
cites work: Existence and uniqueness of traveling waves for non-monotone integral equations with applications
cites work: Spreading speeds and travelling waves for non-monotone time-delayed lattice equations
cites work: Long-Time Behavior of a Class of Biological Models
cites work: Non-local dispersal.
cites work: The evolution of dispersal
cites work: Spreading Speeds and Traveling Waves for Nonmonotone Integrodifference Equations
cites work: Spatial dynamics of a periodic population model with dispersal*
cites work: Random dispersal vs. non-local dispersal
cites work: Spreading speeds as slowest wave speeds for cooperative systems
cites work: Spreading speed, traveling waves, and minimal domain size in impulsive reaction-diffusion models
cites work: The Effect of Dispersal Patterns on Stream Populations
cites work: Entire solutions in the Fisher-KPP equation with nonlocal dispersal
cites work: Spreading speeds and traveling waves in competitive recursion systems
cites work: Asymptotic pattern for a partial neutral functional differential equation
cites work: A nonlocal diffusion model of a single species with age structure
cites work: Asymptotic speeds of spread and traveling waves for monotone semiflows with applications
cites work: Spreading speeds and traveling waves for periodic evolution systems
cites work: Asymptotic speed of propagation and traveling wavefronts in a non-local delayed lattice differential equation
cites work: Abstract Functional Differential Equations and Reaction-Diffusion Systems
cites work: Travelling wave fronts in nonlocal delayed reaction-diffusion systems and applications
cites work: Traveling wave fronts of delayed non-local diffusion systems without quasimonotonicity
cites work: Entire solutions in nonlocal dispersal equations with bistable nonlinearity
cites work: Travelling-front solutions for integro-differential equations. I.
cites work: Spectral theory for general nonautonomous/random dispersal evolution operators
cites work: Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats
cites work: Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats
cites work: Spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in periodic habitats
cites work: Asymptotic patterns of a reaction-diffusion equation with nonlinear-nonlocal functional response
cites work: Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations.
cites work: Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread
cites work: Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction--diffusion models.
cites work: Spreading speeds of spatially periodic integro-difference models for populations with nonmonotone recruitment functions
cites work: Spreading speeds and traveling waves for non-cooperative reaction-diffusion systems
cites work: Q5502258
cites work: Entire solutions for nonlocal dispersal equations with spatio-temporal delay: monostable case
cites work: Spatial dynamics of a nonlocal and delayed population model in a periodic habitat
cites work: Spreading speed and traveling waves for a multi-type SIS epidemic model
cites work: Regular traveling waves for a nonlocal diffusion equation
cites work: Minimal wave speed and uniqueness of traveling waves for a nonlocal diffusion population model with spatio-temporal delays.
cites work: Spreading speeds and uniqueness of traveling waves for a reaction diffusion equation with spatio-temporal delays
cites work: Traveling waves in a convolution model with infinite distributed delay and non-monotonicity
cites work: Travelling wave solutions in non-local convolution diffusive competitive-cooperative systems
cites work: Traveling waves in a nonlocal dispersal population model with age-structure
cites work: Spatial dynamics of a reaction-diffusion model with distributed delay
cites work: The asymptotic speed of spread and traveling waves for a vector disease model
DOI: 10.1007/S10884-016-9555-1