Dynamics Behaviors of a Reaction-Diffusion Predator-Prey System with Beddington-DeAngelis Functional Response and Delay

This paper is concerned with the existence of traveling wave solutions in a reaction-diffusion predator-prey system with Beddington-DeAngelis functional response and a discrete time delay. By introducing a partial quasi-monotonicity condition and constructing a pair of upper-lower solutions, we establish the existence of traveling wave solutions. Moreover, a numerical simulation is carried out to illustrate the theoretical results.

Traveling Waves for an Epidemic Model with Vaccination and Nonlocal Diffusion

An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder's fixed point theorem,sufficient conditions are obtained for the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.

Asymptotic Dynamics of a Single-species Model with Resource-dependent Dispersal in One Dimension

In this paper,we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.To overcome the analytical difficulties brought by the resource-dependent dispersal,we use the idea of changing variables to transform the model into a uniform dispersal one.Then the existence and uniqueness of positive stationary solution to the model can be verified by the squeezing argument,where the solution plays a crucial role in later analyses.Moreover,the asymptotic behavior of solutions to the model is obtained by the upper-lower solutions method.The result indicates that the solutions of the model converge to the corresponding positive stationary solution locally uniformly in one dimension as time goes to infinity.

Asymptotic Behavior of Nonlinear Parabolic Partial Functional Differential Equations

This paper is devoted to the investigation of the asymptotic behavior for a class of nonlinear parabolic partial functional differential equations. The boundedness and stability of the solutions are established by the upper-lower solution method. Some conditions are obtained by using the semigroup theory, the properties of nonnegative matrices and the techniques of inequalities to determine the asymptotically stable region of the equilibrium.

Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity

This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of ＂desirable pair of upper-lower solutions＂, through which a subset can be constructed. We then apply the Schauder＇s fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.

Study on mechanism of fiber grouted material in pre-stressed anchor rope

The fiber grouted material can reinforce the tension strength, shear strength as well as the index of fracture ductile, and remarkably improve the endurance of pre-stressed anchor rope under long-time loading. As a result, it has the better application foreground. Based on the shear log model and Hashin-Shtrikman upper and lower limited theorem, we have studied the mechanism of fiber grouted material applied in pre-stressed anchor rope and material property, and analyzed the effect of resistance strength of bond, resistance distribution of anchor section and the loading-deformation relationship of anchor body.

GLOBAL SOLUTION,ASYMPTOTIC BEHAVIOR AND BLOW-UP PROBLEMS FOR A MODEL OF NUCLEAR REACTORS

The existence of global solution and the blow-up problem for a model of nuclear reactorsare discussed by using the upper-lower solution and energy estimate methods; asymptoticbehavior of global solution is also discussed with the aid of L_p estimate and semigroupmethod for this model. Nice results, which explain the phenomenon of nuclear reactorsbetter, are obtained.

TRAVELING WAVE SOLUTIONS IN A THREE-SPECIES FOOD-CHAIN MODEL WITH DIFFUSION AND DELAYS

This paper deals with the existence of traveling wave solutions in a three-species food-chain model with spatial diffusion and time delays due to gestation and negative feedback. By using a cross iteration scheme and Schauder＇s fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the trivial steady state and the positive steady state. Numerical simulations are carried out to illustrate the main results. In particular, our results extend and improve some known results.

Traveling waves of a delayed HIV/AIDS epidemic model with treatment and spatial diffusion

In this paper,a delayed HIV/AIDS epidemic model with treatment and spatial diffusion is introduced.By analyzing the corresponding characteristic equations,the local stability of a disease-free steady state and an endemic steady state is discussed.By using the cross-iteration method and Schauder’s fixed point theorem,we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions.By constructing a pair of upper-lower solutions,we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.It is shown that the existence of traveling waves of the proposed HIV/AIDS epidemic model is fully determined by the basic reproduction number and the minimal wave speed.Finally,numerical simulations are performed to show the feasibility and effectiveness of the theoretical results.

Minimal wave speed of a diffusive SIR epidemic model with nonlocal delay

This paper is concerned with the minimal wave speed in a diffusive epidemic model with nonlocal delays.We define a threshold.By presenting the existence and the nonexistence of traveling wave solutions for all positive wave speed,we confirm that the threshold is the minimal wave speed of traveling wave solutions,which models that the infective invades the habitat of the susceptible.For some cases,it is proven that spatial nonlocality may increase the propagation threshold while time delay decreases the threshold.

THE EXISTENCE,UNIQUENESS AND STABILITY OF POSITIVE PERIODIC SOLUTION FOR PERIODIC REACTION-DIFFUSION SYSTEM

The existence of periodic solutions for periodic reaction-diffusion systems with time delay by the periodic upper-lower solution method is investigated. Some methods for proving the uniqueness and the stability of the periodic solution are also given. Two examples are used to show how to use our methods.

TRAVELING WAVES IN A REACTION-DIFFUSION PREDATOR-PREY SYSTEM WITH NONLOCAL DELAYS

This paper is concerned with the existence of traveling wave solutions in a reaction- diffusion predator-prey system with nonlocal delays. By introducing a partially expo- nential quasi-monotonicity condition and a new cross iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a desirable pair of upper-lower solutions, we establish the existence of traveling wave solutions. Finally, some numerical examples are carried out to illustrate the theoretical results.