Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations

From MaRDI portal
Publication:1408597

zbMath1023.35513MaRDI QIDQ1408597

Xinfu Chen

Publication date: 25 September 2003

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




Related Items

Almost periodic traveling waves of nonlocal evolution equationsAn Ambrosetti-Prodi type result for integral equations involving dispersal operatorsExistence and stability of traveling curved fronts for nonlocal dispersal equations with bistable nonlinearitySpiral traveling wave solutions of nonlinear diffusion equations related to a model of spiral cyrstal growthStability of bistable traveling wavefronts for a three species competitive-cooperative system with nonlocal dispersalTraveling wave solutions in advection hyperbolic-parabolic system with nonlocal delayTraveling waves for a nonlocal dispersal predator-prey model with two preys and one predatorGlobal dynamics of an SIR epidemic model with nonlocal diffusionAsymptotic speeds of spread for a nonlocal diffusion equationPlant dynamics, birth-jump processes, and sharp traveling wavesTraveling waves of a Lotka-Volterra strong competition system with nonlocal dispersalA counterexample to the Liouville property of some nonlocal problemsGlobal stability of traveling wave fronts for non-local delayed lattice differential equationsNonlinear stability of traveling wave fronts for delayed reaction diffusion systemsRegularity of transition fronts in nonlocal dispersal evolution equationsMonotonicity, asymptotic behaviors and uniqueness of traveling waves to a nonlocal dispersal equation modeling an age-structured populationExistence, uniqueness and asymptotic behavior of traveling wave fronts for a generalized Fisher equation with nonlocal delayTraveling waves of a nonlocal dispersal Kermack-McKendrick epidemic model with delayed transmissionTravelling waves of nonlocal isotropic and anisotropic diffusive epidemic models with temporal delayProperties of traveling wave fronts for three species Lotka-Volterra systemExistence and non-existence of traveling wave solutions for a nonlocal dispersal SIR epidemic model with nonlinear incidence rateNumerical simulations of traveling and stationary wave solutions arising from reaction-diffusion population models with delay and nonlocalityTravelling fronts in integrodifferential equationsTraveling waves for monotone or non-monotone equations with nonlocal delays in a cylinderFronts between periodic patterns for bistable recursions on latticesWell-posedness for a system of integro-differential equationsSpreading speeds for a class of non-local convolution differential equationEntire solutions for a reaction-diffusion equation with doubly degenerate nonlinearityExistence and uniqueness of forced waves in a delayed reaction-diffusion equation in a shifting environmentTraveling waves in time almost periodic structures governed by bistable nonlinearities. I: Stability and UniquenessTraveling waves in time almost periodic structures governed by bistable nonlinearities. II: ExistenceExistence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks.Propagation, diffusion and free boundariesGlobal stability of travelling waves for a class of monostable epidemic modelsTraveling wave solutions for a delayed SIRS infectious disease model with nonlocal diffusion and nonlinear incidenceEstimate of the travelling wave speed for an integro-differential equationA nonlocal Dirichlet problem with impulsive action: estimates of the growth for the solutionsEffect of harvesting quota and protection zone in a nonlocal dispersal reaction-diffusion equationLocalized radial basis functions-based pseudo-spectral method (LRBF-PSM) for nonlocal diffusion problemsWave propagation in a infectious disease model with non-local diffusionEntire solutions in nonlocal monostable equations: asymmetric caseAsymptotic behavior of spreading fronts in the anisotropic Allen-Cahn equation on \(\mathbb{R}^n\)Traveling wave solutions in a nonlocal dispersal SIR epidemic model with general nonlinear incidencePropagation dynamics of an anisotropic nonlocal dispersal equation with delayed nonlocal responseTraveling waves in delayed reaction-diffusion equations in biologySemi-wave and spreading speed of the nonlocal Fisher-KPP equation with free boundariesMultidimensional stability of traveling fronts in combustion and non-KPP monostable equationsHindrances to bistable front propagation: application to \textit{Wolbachia} invasionMonostable waves in a class of non-local convolution differential equationNonlinear stability of traveling waves in a monostable epidemic model with delayAsymptotic spreading of a time periodic diffusion equation with degenerate monostable nonlinearityCritical extinction exponents for a nonlocal reaction-diffusion equation with nonlocal source and interior absorptionTraveling fronts for lattice neural field equationsBistable waves of a recursive system arising from seasonal age-structured population modelsInvasion fronts on graphs: the Fisher-KPP equation on homogeneous trees and Erdős-Réyni graphsTraveling wave solutions of a nonlocal dispersal predator-prey model with spatiotemporal delayGeneralized fronts in reaction-diffusion equations with bistable nonlinearitySpreading speeds and traveling waves for a nonlocal dispersal equation with convolution-type crossing-monostable nonlinearityEntire solutions for nonlocal dispersal equations with spatio-temporal delay: monostable casePropagation speed of travelling fronts in non local reaction-diffusion equationsWave propagation in a nonlocal diffusion epidemic model with nonlocal delayed effectsMultidimensional stability of disturbed pyramidal traveling fronts in the Allen-Cahn equationEntire solutions for nonlocal dispersal equations with bistable nonlinearity: asymmetric caseExistence and uniqueness of entire solutions for a reaction-diffusion equationPropagation and its failure in a lattice delayed differential equation with global interactionPropagation phenomena for a two-species Lotka-Volterra strong competition system with nonlocal dispersalThe motion of weakly interacting localized patterns for reaction-diffusion systems with nonlocal effectPulsating waves in a dissipative medium with delta sources on a periodic latticeEntire solutions originating from multiple fronts of an epidemic model with nonlocal dispersal and bistable nonlinearityPropagation phenomena in monostable integro-differential equations: acceleration or not?Entire solutions originating from monotone fronts for nonlocal dispersal equations with bistable nonlinearityPropagation dynamics of nonlocal dispersal equations with inhomogeneous bistable nonlinearityPeriodic traveling fronts for partially degenerate reaction-diffusion systems with bistable and time-periodic nonlinearityRevisit of the Peierls-Nabarro model for edge dislocations in Hilbert spaceDynamics of a nonlocal diffusive logistic model with free boundaries in time periodic environmentWavefronts of a nonlocal state-dependent time delay modelStability of traveling waves of the nonlocal Fisher-KPP equationUniqueness and stability of traveling wave fronts for an age-structured population model in a 2D lattice stripTraveling waves in time periodic lattice differential equationsGlobal stability of traveling wave fronts in a two-dimensional lattice dynamical system with global interactionExistence of solution for a nonlocal dispersal model with nonlocal term via bifurcation theoryAxisymmetric traveling fronts in balanced bistable reaction-diffusion equationsGlobal solutions for bistable degenerate reaction-diffusion equation with time-delay and nonlocal effectUniqueness of wave speeds in bistable reaction-diffusion equationsInvasion waves for a nonlocal dispersal predator-prey model with two predators and one preyLogarithmic corrections in Fisher-KPP type porous medium equationsTraveling waves in a nonlocal dispersal predator-prey modelStability of traveling waves in a population dynamic model with delay and quiescent stagePersistence and propagation of a discrete-time map and PDE hybrid model with strong Allee effectGlobal asymptotic stability of traveling waves to the Allen-Cahn equation with a fractional LaplacianNonlinear nonlocal reaction-diffusion problem with local reactionGlobal asymptotic stability of constant equilibrium in a nonlocal diffusion competition model with free boundariesHomoclinic solutions to an integral equation: Existence and stabilityMetastability and stability of patterns in a convolution model for phase transitionsMultiscale analysis for traveling-pulse solutions to the stochastic FitzHugh-Nagumo equationsMultiple layered solutions of the nonlocal bistable equationBistable traveling waves in a delayed competitive systemDynamics of solutions of a diffusive time-delayed HIV/AIDS epidemic model: traveling wave solutions and spreading speedsSpectral analysis and multidimensional stability of traveling waves for nonlocal Allen--Cahn equation.Exponential stability of traveling waves for a nonlocal dispersal SIR model with delayInvasion traveling wave solutions in temporally discrete random-diffusion systems with delaysExistence and stability of traveling waves for Leslie-Gower predator-prey system with nonlocal diffusionAre buffers boring? Uniqueness and asymptotical stability of traveling wave fronts in the buffered bistable systemExistence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delayExistence of traveling waves in the fractional bistable equationOn the principal eigenvalue of some nonlocal diffusion problemsUniqueness and stability of traveling waves for a three-species competition system with nonlocal dispersalStability of traveling wavefronts for a discrete diffusive competition system with three speciesGlobal stability of non-monotone traveling wave solutions for a nonlocal dispersal equation with time delayExistence, uniqueness and stability of transition fronts of non-local equations in time heterogeneous bistable mediaExistence and stability of bistable wavefronts in a nonlocal delayed reaction–diffusion epidemic systemV-shaped traveling fronts of fractional Allen–Cahn equationsExistence, uniqueness and asymptotic stability of traveling wavefronts in a non-local delayed diffusion equationTraveling wave dynamics for Allen-Cahn equations with strong irreversibilityAsymptotic behavior for nonlocal diffusion equationsTraveling waves in delayed predator-prey systems with nonlocal diffusion and stage structurePropagation and reaction–diffusion models with free boundariesGlobal stability of traveling wave fronts for a reaction–diffusion system with a quiescent stage on a one-dimensional spatial latticeTravelling wave solutions for a nonlocal dispersal HIV infection dynamical modelBistable traveling waves in impulsive reaction-advection-diffusion modelsSpatial propagation in nonlocal dispersal Fisher-KPP equationsSharp estimates for the spreading speeds of the Lotka-Volterra diffusion system with strong competitionEntire solutions with annihilating fronts to a nonlocal dispersal equation with bistable nonlinearity and spatio-temporal delayEntire solutions of time periodic bistable reaction-advection-diffusion equations in infinite cylindersPropagation dynamics in an integro-differential Fisher-KPP equation with degenerated reaction functionsValidity of amplitude equations for nonlocal nonlinearitiesTraveling wave solutions of a nonlocal dispersal SIRS model with spatio-temporal delayTraveling Pulses in a Nonlocal Equation Arising Near a Saddle-Node Infinite Cycle BifurcationThreshold convergence results for a nonlocal time-delayed diffusion equationStability, uniqueness and recurrence of generalized traveling waves in time heterogeneous media of ignition typeExistence of periodic traveling waves in a nonlocal convection-diffusion model with chemotaxis and delay effectWave propagation for a non-cooperative system with nonlocal dispersal and a cyclic structureA time-periodic competition model with nonlocal dispersal and bistable nonlinearity: propagation dynamics and stabilityExistence, uniqueness and stability of forced waves to the Lotka‐Volterra competition system in a shifting environmentInteraction of traveling curved fronts in bistable reaction-diffusion equations in \(\mathbb{R}^2\)Global stability of critical-speed pulsating fronts for degenerate monostable reactionsTime-periodic traveling waves for a periodic Lotka-Volterra competition system with nonlocal dispersalNonlinear stability of traveling waves for a multi-type SIS epidemic modelPlanar Propagating Terraces and the Asymptotic One-dimensional Symmetry of Solutions of Semilinear Parabolic EquationsPropagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on ℝSlowing Allee effect versus accelerating heavy tails in monostable reaction diffusion equationsLarge time behavior of the solutions with spreading fronts in the Allen-Cahn equations on \(\mathbb{R}^n\)Existence and asymptotic behavior of invasion wave solutions in temporally discrete diffusion systems with delaysLongtime Behavior of Solutions of a SIS Epidemiological ModelPropagation dynamics of nonlocal dispersal equations with bistable nonlinearity in spatially periodic mediaSpeed of wave propagation for a nonlocal reaction–diffusion equationUniqueness and global stability of forced waves in a shifting environmentPulsating fronts for nonlocal dispersion and KPP nonlinearityEntire solutions for a delayed nonlocal dispersal system with monostable nonlinearitiesMutual inclusion in a nonlocal competitive Lotka Volterra systemMinimal wave speed of a nonlocal diffusive epidemic model with temporal delayA nonlocal inhomogeneous dispersal processTraveling Waves and Pattern Formation for Spatially Discrete Bistable Reaction-Diffusion EquationsWave propagation for a class of non-local dispersal non-cooperative systemsExistence and exponential stability of traveling waves for delayed reaction-diffusion systemsA nonlocal convection-diffusion equationHow to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problemsEntire solutions for bistable lattice differential equations with obstaclesBistable wavefronts in a diffusive and competitive Lotka-Volterra type system with nonlocal delaysA nonlocal nonlinear diffusion equation with blowing up boundary conditionsGlobal convergence toward traveling fronts in nonlinear parabolic systems with a gradient structureDynamical systems and traveling waves in almost periodic structuresNeumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete modelsSpatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equationsTraveling curved fronts of anisotropic curvature flowsSpectral methods for mesoscopic models of pattern formationA General Framework for Stochastic Traveling Waves and Patterns, with Application to Neural Field EquationsUnnamed ItemTraveling waves for a nonlocal dispersal SIR model with standard incidenceUnnamed ItemA Free Boundary Problem for Corporate Bond Pricing and Credit Rating Under Different Upgrade and Downgrade ThresholdsStability of traveling waves of a diffusive susceptible-infective-removed (SIR) epidemic modelAsymptotic Profiles of Solutions and Propagating Terrace for a Free Boundary Problem of Nonlinear Diffusion Equation with Positive Bistable NonlinearityThe Decay Rates of Traveling Waves and Spectral Analysis for a Class of Nonlocal Evolution EquationsTraveling wavefronts in nonlocal dispersal and cooperative Lotka-Volterra system with delaysEntire solutions in bistable reaction-diffusion equations with nonlocal delayed nonlinearityCritical blow-up exponents for a nonlocal reaction-diffusion equation with nonlocal source and interior absorptionStability of traveling wave fronts for nonlocal diffusive systemsExistence of bistable waves for a nonlocal and nonmonotone reaction-diffusion equationExistence and Uniqueness of Traveling Fronts in Lateral Inhibition Neural Fields with Sigmoidal Firing RatesThe dynamics of a Fisher-KPP nonlocal diffusion model with free boundariesBlowup for nonlocal nonlinear diffusion equations with Dirichlet condition and a sourcePropagation dynamics in a three-species competition model with nonlocal anisotropic dispersalExistence and uniqueness of a wavefront in a delayed hyperbolic-parabolic modelExistence, uniqueness and stability of travelling waves in a discrete reaction --- diffusion monostable equation with delayErratum to ``Bistable waves in an epidemic modelAxially asymmetric traveling fronts in balanced bistable reaction-diffusion equationsHeteroclinic solutions of a van der Waals model with infinite nonlocal interactionsTraveling waves of some Holling-Tanner predator-prey system with nonlocal diffusionPropagation acceleration in reaction diffusion equations with anomalous diffusionsOn an integro-differential model for pest control in a heterogeneous environmentUniqueness and stability of bistable waves for monotone semiflowsMULTIDIMENSIONAL STABILITY OF PLANAR WAVES FOR DELAYED REACTION-DIFFUSION EQUATION WITH NONLOCAL DIFFUSIONUnnamed ItemTraveling waves in a delayed SIR model with nonlocal dispersal and nonlinear incidenceThe stability of traveling waves for Allen–Cahn equations with fractional LaplacianTraveling waves in a nonlocal dispersal SIR epidemic modelOn a nonlocal Cahn–Hilliard model permitting sharp interfacesExistence and asymptotic stability of traveling fronts for nonlocal monostable evolution equationsA phase field approach for direct calculation of interfacial free energy of solid-gas and solid-liquid interfaces in Lennard-Jones systemsImpact of nonlocal dispersal and time periodicity on the global exponential stability of bistable traveling wavesPropagation phenomena with nonlocal diffusion in presence of an obstacleQuantifying the Threshold Phenomenon for Propagation in Nonlocal Diffusion EquationsPropagation phenomena for nonlocal dispersal equations in exterior domainsBistable traveling waves in degenerate competitive systemsGlobal exponential stability of bistable traveling waves in a reaction-diffusion system with cubic nonlinearityAsymptotic behavior of nonlocal bistable reaction-diffusion equationsConvergence to sharp traveling waves of solutions for Burgers-Fisher-KPP equations with degenerate diffusionExistence and stability of traveling wavefronts for a three‐species Lotka–Volterra competitive‐cooperative system with nonlocal dispersalGlobal dynamics and traveling wave solutions for a three‐species modelStability of Front Solutions of the Bidomain Allen–Cahn Equation on an Infinite StripStability of planar traveling waves for a class of Lotka-Volterra competition systems with time delay and nonlocal reaction termGlobal stability of bistable traveling wavefronts for a three-species Lotka–Volterra competition system with nonlocal dispersalExistence, uniqueness and stability of forced waves for asymptotical KPP equations with the nonlocal dispersal in a shifting habitatTraveling fronts in a reaction-diffusion equation with a memory termExponential dichotomies for nonlocal differential operators with infinite range interactionsTraveling waves for a nonlocal dispersal SIR model with delay and external suppliesNonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions\(L^{2}\)-stability of traveling wave solutions to nonlocal evolution equationsMonotone wavefronts for partially degenerate reaction-diffusion systemsExistence and stability of traveling wavefronts in a nonlocal diffusion equation with delayExistence and nonexistence of traveling waves for a nonlocal monostable equationExistence of traveling wave solutions for a nonlocal bistable equation: an abstract approachPinning and unpinning in nonlocal systemsEntire solutions with merging fronts to reaction-diffusion equationsBoundary fluxes for nonlocal diffusionGlobal asymptotic stability of bistable traveling fronts in reaction-diffusion systems and their applications to biological modelsTraveling wavefronts of competing pioneer and climax model with nonlocal diffusionPersistence of wavefronts in delayed nonlocal reaction-diffusion equationsOn a simple criterion for the existence of a principal eigenfunction of some nonlocal operatorsThe role of multiple microscopic mechanisms in cluster interface evolutionLongtime behavior of nonlocal Cahn-Hilliard equationsWave speed analysis of traveling wave fronts in delayed synaptically coupled neuronal networksTraveling waves for delayed non-local diffusion equations with crossing-monostabilityTunneling in two dimensionsTraveling waves for a nonlocal anisotropic dispersal equation with monostable nonlinearityNonlinear stability of traveling wavefronts in an age-structured population model with nonlocal dispersal and delayExistence and uniqueness of traveling waves for fully overdamped Frenkel-Kontorova modelsUniqueness and stability of traveling waves for cellular neural networks with multiple delaysAn integro-differential equation model for the spread of alcohol abuseExponential stability of traveling fronts in a diffusion epidemic system with delaySpreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearityStability of traveling waves in a population dynamics model with spatio-temporal delayPatchy invasion of stage-structured alien species with short-distance and long-distance dispersalFujita exponents for evolution problems with nonlocal diffusionTraveling wavefronts in a bistable reaction diffusion system with spatio-temporal delayFront-like entire solutions for equations with convectionBistable wave fronts in integrodifference equationsGlobal stability of wavefronts with minimal speeds for nonlocal dispersal equations with degenerate nonlinearityLarge time behavior of disturbed planar fronts in the Allen-Cahn equationNonlinear stability of traveling wave fronts for nonlocal delayed reaction-diffusion equationsBlow-up for the non-local \(p\)-Laplacian equation with a reaction termCritical exponent for nonlocal diffusion equations with Dirichlet boundary conditionTraveling waves in a nonlocal diffusion system with delays and partial quasi-monotonicityRegular traveling waves for a nonlocal diffusion equationStability of traveling wave fronts for nonlocal delayed reaction diffusion systemsA nonlocal nonlinear diffusion equation in higher space dimensionsOn uniqueness and monotonicity of solutions of non-local reaction diffusion equationExistence of pulses in excitable media with nonlocal couplingTraveling wave fronts of delayed non-local diffusion systems without quasimonotonicityA nonlocal \(p\)-Laplacian evolution equation with Neumann boundary conditionsTraveling fronts in monostable equations with nonlocal delayed effectsExistence and uniqueness of traveling wave for accelerated Frenkel-Kontorova modelTraveling waves in the discrete fast buffered bistable systemTraveling wave solutions of Allen-Cahn equation with a fractional LaplacianA nonlocal diffusion model of a single species with age structureA non-local bistable reaction-diffusion equation with a gapTransition fronts and stretching phenomena for a general class of reaction-dispersion equationsTransition fronts in nonlocal equations with time heterogeneous ignition nonlinearityTraveling waves in discrete periodic media for bistable dynamicsTraveling wave solutions for bistable fractional Allen-Cahn equations with a pyramidal frontA one-dimensional symmetry result for a class of nonlocal semilinear equations in the planeOn the preservation of cooperation in two-strategy games with nonlocal interactionsApproximating the traveling wavefront for a nonlocal delayed reaction-diffusion equationGlobal asymptotic stability of pushed traveling fronts for monostable delayed reaction-diffusion equationsBistable traveling waves for a competitive-cooperative system with nonlocal delaysEntire solutions in reaction-advection-diffusion equations in cylindersAsymptotic behavior of traveling fronts and entire solutions for a nonlocal monostable equationEntire solutions in monostable reaction-advection-diffusion equations in infinite cylindersSpeeds of traveling waves in some integro-differential equations arising from neuronal networksExistence, uniqueness and asymptotic stability of time periodic traveling waves for a periodic Lotka-Volterra competition system with diffusionDynamics of neuronal wavesExistence and asymptotic stability of traveling waves of discrete quasilinear monostable equationsAsymptotic behavior for nonlocal dispersal equationsSpectrum of some integro-differential operators and stability of travelling wavesEntire solutions in nonlocal dispersal equations with bistable nonlinearityTraveling waves in a nonlocal dispersal population model with age-structureExistence and global stability of traveling curved fronts in the Allen-Cahn equationsAsymptotic stability of traveling waves in a discrete convolution model for phase transitionsTraveling waves in delayed lattice dynamical systems with competition interactionsInfluence of sodium currents on speeds of traveling wave fronts in synaptically coupled neuronal networksSpreading speeds for monostable equations with nonlocal dispersal in space periodic habitatsInterface conditions for a phase field model with anisotropic and non-local interactionsEntire solutions in the Fisher-KPP equation with nonlocal dispersalExponential stability of traveling waves in a nonlocal dispersal epidemic model with delayAsymptotic behavior and uniqueness of traveling wave fronts in a delayed nonlocal dispersal competitive systemRegularity and stability of transition fronts in nonlocal equations with time heterogeneous ignition nonlinearityStability and uniqueness of traveling wavefronts in a two-dimensional lattice differential equation with delayBlow-up for a non-local diffusion problem with Neumann boundary conditions and a reaction termThe uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equationsBistable traveling waves for monotone semiflows with applicationsThe limit as \(p \rightarrow \infty \) in a nonlocal \(p\)-Laplacian evolution equation: a nonlocal approximation of a model for sandpilesEntire solutions of reaction-advection-diffusion equations with bistable nonlinearity in cylindersTraveling waves in lattice dynamical systemsGlobal existence of solutions to the Fowler equation in a neighbourhood of travelling-wavesAsymptotic stability of traveling wave fronts in nonlocal reaction-diffusion equations with delayCoupling local and nonlocal evolution equationsAsymptotic expansions for nonlocal diffusion equations in \(L^q\)-norms for \(1\leqslant q\leqslant 2\)Travelling waves in monostable and bistable stochastic partial differential equationsBistable wave fronts in a stage-structured reaction-diffusion model for a single species with distributed maturation delayMaximum and antimaximum principles for some nonlocal diffusion operatorsBlowing up boundary conditions for a nonlocal nonlinear diffusion equation in several space dimensionsMultidimensional stability of planar traveling waves for the scalar nonlocal Allen-Cahn equationMulti-type entire solutions in a nonlocal dispersal epidemic modelAn inhomogeneous nonlocal diffusion problem with unbounded steps




This page was built for publication: Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations