GLOBAL STABILITY OF TRAVELING WAVEFRONTS FOR NONLOCAL REACTION-DIFFUSION EQUATIONS WITH TIME DELAY

This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts （waves with speeds c 〉 c＊, where c=c＊ is the minimal speed） is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x → -∞, but it can be allowed arbitrary large in other locations, which improves the results in[9, 18, 21].

REMARK ON CRITICAL SPEED OF TRAVELING WAVEFRONTS FOR NICHOLSON'S BLOWFLIES EQUATION WITH DIFFUSION

This note is devoted to the son＇s blowflies equation with diffusion, a critical speed of traveling waves, we give behavior with respect to the mature age study on the traveling wavefronts to the Nicholtime-delayed reaction-diffusion equation. For the a detailed analysis on its location and asymptotic

Traveling wavefronts for a reaction-diffusion-chemotaxis model with volume-filling effect

In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for the patterns, which show that a local perturbation at the constant steady state is spread over the whole domain in the form of a traveling wavefront. The simulations demonstrate that the amplitude equations capture the evolution of the exact patterns obtained by numerically solving the considered system.

The dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria

In this paper,we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria.We first establish the existence of spreading speed,and show that the spreading speed coincides with the minimal wave speed of traveling wavefronts.Moreover,a lower bound estimate of the spreading speed is given.Then,we prove that the traveling wavefronts with large speeds are globally exponentially stable,when the initial perturbation around the traveling wavefronts decays exponentially asχ→-∞,but the initial perturbation can be arbitrarily large in other locations.The adopted methods are the weighted energy and the squeezing technique.

Global stability of bistable traveling wavefronts for a three-species Lotka-Volterra competition system with nonlocal dispersal

This paper is devoted to the study of traveling wavefronts for a three-component Lotka-Volterra system with nonlocal dispersal.This system arises in the study of three-species competition model in which there is no competition between two of these three species.It has been shown that this system admits a bistable traveling wavefront.In this paper,we further investigate the stability of bistable traveling wavefronts.By constructing suitable super-and sub-solutions and using a dynamical system approach,we obtain the globally asymptotic stability of the bistable traveling wavefronts.

Traveling wavefronts of a nonlinear reaction-diffusion model of tumor growth under the acid environment

In this paper, a reaction-diffusion model describing temporal development of tumor tissue, normal tissue and excess H＋ ion concentration is considered. Based on a combi- nation of perturbation methods, the Fredholm theory and Banach fixed point theorem, we theoretically justify the existence of the traveling wave solution for this model.

TRAVELLING WAVEFRONTS IN DELAYED COOPERATIVE AND DIFFUSIVE SYSTEMS WITH NON-LOCAL EFFECTS

In this paper, traveling wavefront solutions are established for two cooperative systems with time delay and non-local effects. The results are an extension of the existing results for delayed logistic scale equations and diffusive Nicholson equations with non-local effects to systems. The approach used is the upper-lower solution technique and Schauder fixed point Theorem developed by Ma（J Differential Equations,2001,171：294-314. ）.

Wavefront solutions in diffusive Nicholson’s blowflies equation with nonlocal delay

This paper is concerned with the diffusive Nicholson＇s blowflies equation with nonlocal delay incorporated as an integral convolution over the entire past time up to now and the whole one-dimensional spatial domain R. Assume that the delay kernel is a strong generic kernel. By the linear chain techniques and the geometric singular perturbation theory, the existence of travelling front solutions is shown for small delay.

Wavefronts of a Nonlocal State-dependent Time Delay Model

This paper is concerned with the travelling wavefronts of a nonlocal dispersal cooperation model with harvesting and state-dependent delay,which is assumed to be an increasing function of the population density with lower and upper bound.Especially,state-dependent delay is introduced into a nonlocal reaction-diffusion model.The conditions of Schauder's fixed point theorem are proved by constructing a reasonable set of functionsΓ(see Section 2)and a pair of upper-lower solutions,so the existence of traveling wavefronts is established.The present study is continuation of a previous work that highlights the Laplacian diffusion.

Visualization of ultrasonic traveling wavefront by CW modulated laser diode

A new method is presented to display ultrasonic traveling wavefront by colltinuously modulated laser diode based on the temporal correlation theory. It is proved by experimeot.

Entire solutions for some reaction-diffusion systems

This paper is concerned with the existence of entire solutions of some reaction-diffusion systems. We first consider Belousov-Zhabotinskii reaction model. Then we study a general model. Using the comparing argument and sub-super-solutions method, we obtain the existence of entire solutions which behave as two wavefronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables. At last, we give some examples to explain our results for the general models.