Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction--diffusion models.
type: Item
instance of: scholarly article
title: Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction--diffusion models.
zbMATH Open document ID: 1045.45009
DOI: 10.1016/S0022-0396(03)00175-X
author: Horst R. Thieme
author: Xiao-Qiang Zhao
published in: Journal of Differential Equations
publication date: 2004-01-26T00:00:00Z
review text: The author extends a lot of results obtained earlier in the theory of asymptotic speeds of spread and monotone traveling waves to the class of nonlinear integral equations of the form \[ u(t,x)= u_0(t, x)+ \int^t_0 \int_{\mathbb R^n} F(u(t- s,x- y),s,y)\,dy\,ds,\tag{1} \] where \(F(u,s,y)= F: \mathbb R^2_+\times \mathbb R^n\to \mathbb R\) is continuous in \(u\) and Borel measurable in \((s,y)\). A lot of results concerning (1) are obtained under various additional assumptions concerning the function \(F\). The obtained results are applied to some time-delayed reaction and diffusion population models.
reviewed by: Józef Banaś
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 45M20
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 2032996
zbMATH Keywords: Nonlinear integral equations
zbMATH Keywords: Asymptotic speeds of spread
zbMATH Keywords: Traveling waves
zbMATH Keywords: Minimal wave speeds
zbMATH Keywords: Population models
zbMATH Keywords: Positive solution
MaRDI profile type: Publication
cites work: Monotone travelling fronts in an age-structured reaction-diffusion model of a single species
cites work: Q4134311
cites work: Q4089232
cites work: Multidimensional nonlinear diffusion arising in population genetics
cites work: Deterministic epidemic waves
cites work: Deterministic epidemic waves of critical velocity
cites work: Convergence to equilibrium states for a reaction-diffusion system modelling the spatial spread of a class of bacterial and viral diseases
cites work: Saddle point behaviour for a reaction-diffusion system: Application to a class of epidemic models
cites work: Q3200920
cites work: Analysis of a Reaction-Diffusion System Modeling Man--Environment--Man Epidemics
cites work: Thresholds and travelling waves for the geographical spread of infection
cites work: Run for your life. A note on the asymptotic speed of propagation of an epidemic
cites work: On the bounded solutions of a nonlinear convolution equation
cites work: Q4272982
cites work: Wavefronts and global stability in a time-delayed population model with stage structure
cites work: Spreading speed and linear determinacy for two-species competition models
cites work: Biological growth and spread modeled by systems of recursions. I: Mathematical theory
cites work: Biological growth and spread modeled by systems of recursions. II: Biological theory
cites work: Traveling wavefronts for delayed reaction-diffusion systems via a fixed point theorem
cites work: Abstract Functional Differential Equations and Reaction-Diffusion Systems
cites work: Q3994920
cites work: Wave solutions for the deterministic non-reducible n-type epidemic
cites work: The uniqueness of wave solutions for the deterministic non-reducible n- type epidemic
cites work: The asymptotic speed of propagation of the deterministic non-reducible n- type epidemic
cites work: Asymptotic Behavior and Traveling Wave Solutions for Parabolic Functional Differential Equations
cites work: Strongly order preserving semiflows generated by functional differential equations
cites work: Global Asymptotic Stability of Traveling Waves in Delayed Reaction-Diffusion Equations
cites work: A reaction–diffusion model for a single species with age structure. I Travelling wavefronts on unbounded domains
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: On a class of Hammerstein integral equations
cites work: Q4420178
cites work: A non-local delayed and diffusive predator-prey model.
cites work: The velocity of spatial population expansion
cites work: Propagation of frontal polymerization—crystallization waves
cites work: Remark on the preceding paper of Serrin
cites work: Long-Time Behavior of a Class of Biological Models
cites work: Analysis of linear determinacy for spread in cooperative models
cites work: Theory and applications of partial functional differential equations
cites work: Diffusive monotonicity and threshold dynamics of delayed reaction diffusion equations
cites work: Traveling wave fronts of reaction-diffusion systems with delay
cites work: Fisher waves in an epidemic model
full work available at URL: s0022-0396(03)00175-x
OpenAlex ID: W2067809216
description: scientific article; zbMATH DE number 2032996