单种群杆菌生长反应扩散型动力学方程的数值模拟研究

Based on the theories of cellar biology a reaction-diffusion-like dynamic equation valid for the popular growth of single bacillus was established by means of the nonlinear method of the dynamic systems.Furthermore,the investigations of numerical simulations and experiments of this evolutionary equation were analysised.These exploratory results are helpful to complete the biological wave theory.

反应扩散型变分不等方程的一个分歧定理

给出非线性算子为某种α Lipschitz (k =d 2 2 )时的分歧定理 .

扰动反应扩散型方程的近似对称约化

利用近似的广义条件对称方法研究扰动的反应扩散型方程的近似对称约化问题,得到所研究方程完全的分类并借助于近似广义条件对称将扰动的偏微分方程约化为扰动的常微分方程组.

组元配比对球磨固态燃烧式反应和扩散型反应的影响

采用搅拌式高能球磨机研究了不同铝含量的Al/CuO球磨固态燃烧反应和Al -Cu及Al-Cu -Al2 O3 扩散型反应 .结果表明 :理想配比的Al/CuO的反应孕育期最短 ,偏离这一配比 ,孕育期延长 ,反应由整体燃烧式逐渐过渡到渐进燃烧式完成 ;球磨强度扩大以燃烧式进行的组元配比范围 ;当铝含量超过理想配比中的比例 ,随Al含量增加 ,反应由单一的还原反应向还原 +合成复合反应模式转化 ,反应产物为平衡组织 ,依次为Cu +Al2 O3、Cu9Al4 +Al2 O3、CuAl2 +Al2 O3、Al(Cu) +Al2 O3;而球磨Al-Cu和Al-Cu -Al2 O3 体系的反应以扩散方式进行 。

一类奇异摄动抛物型反应扩散问题的数值解

奇异摄动问题一直需要高精度的数值方法,本文提出了重心拉格朗日插值配点法来求解一类奇异摄动抛物型反应扩散问题,与其他方法相比,数值实验表明该方法是解决这类问题的一种高精度方法。

拟单调中立型反应扩散方程行波解的唯一性

本文考虑了具有拟单调反应项的中立型反应扩散方程行波解的唯一性问题。首先通过线性变换将方程化为具有无限离散时滞的反应扩散方程,并利用Ikehara定理得到了无限时滞方程波速 的单调行波解的指数渐近性态,进而得到方程波速 的单调行波解是唯一的(平移意义下),最后根据两类方程的解之间的联系得到了原中立型方程波速 的单调行波解的唯一性(平移意义下)。

一类界面化学反应模型的解的渐近性

本文建立了一个界面化学反应模型，这个模型是一个具有非线性边界条件的抛物型反应扩散方程组．通过建立并求解关于方程组的解的微分不等式，我们得到了解及其任意阶导数在Ｌ∞的收敛速率估计．

Diffusion and Reaction Model of Catalyst Pellets for Fischer-Tropsch Synthesis

The diffusion and reaction phenomenon in a Fe-based catalyst pellet for Fischer-Tropsch synthesis was studied. It was considered that the pores of catalyst pellets were full of liquid wax under Fischer-Tropsch synthesis conditions. The re- actants diffused from the bulk gas phase to the external surface of the pellet, and then the reactants diffused through the wax inside the pellet and reacted on the internal surface formed along the pore passages of the pellet. On the basis of reaction kinetics and double a-ASF product distribution model, a diffusion and reaction model of catalyst pellet was established. The effects of diffusion and reaction interaction in a catalyst pellet, the bulk temperature, the reaction pressure and the pellet size on the reactivity were further investigated. The relationship between the internal diffusion effectiveness factor of spherical catalyst pellet and the Thiele modulus were also discussed. The bulk temperature and pellet size have significant effects on the reactivity, while the pressure shows only a slight influence on the reactivity. The internal diffusion effectiveness factor decreases with an increasing Thiele modulus.

Turing Patterns in a Reaction-Diffusion System

We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel Epstein model Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.

Qualitative analysis for a Wolbachia infection model with diffusion

We consider a reaction-diffusion model which describes the spatial Wolbachia spread dynamics for a mixed population of infected and uninfected mosquitoes. By using linearization method, comparison principle and Leray-Schauder degree theory, we investigate the influence of diffusion on the Wolbachia infection dynamics.After identifying the system parameter regions in which diffusion alters the local stability of constant steadystates, we find sufficient conditions under which the system possesses inhomogeneous steady-states. Surprisingly,our mathematical analysis, with the help of numerical simulations, indicates that diffusion is able to lower the threshold value of the infection frequency over which Wolbachia can invade the whole population.

Qualitative Analysis on a Reaction-Diffusion Prey-Predator Model and the Corresponding Steady-States

The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem. The local and global stability of the positive constant steady-state are discussed, and then some results for non- existence of positive non-constant steady-states are derived.

Existence, uniqueness and stability of pyramidal traveling fronts in reaction-diffusion systems

In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various nonlinearities. In this paper, by using the comparison argument and constructing appropriate super- and subsolutions, we study the existence, uniqueness and stability of three- dimensional traveling fronts of pyramidal shape for monotone bistable systems of reaction-diffusion equations in R3. The pyramidal traveling fronts are characterized as either a combination of planar traveling fronts on the lateral surfaces or a combination of two-dimensional V-form waves on the edges of the pyramid. In particular, our results are applicable to some important models in biology, such as Lotk,u-Volterra competition-diffusion systems with or without spatio-temporal delays, and reaction-diffusion systems of multiple obligate mutualists.

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.

On a non-autonomous reaction-convection diffusion model to study the bacteria distribution in a river

In this paper, we propose a non-autonomous convection-reaction diffusion system （CDI） with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria （ARB） in a river. The main contributions of this paper are： （i） the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system （CDI）e, （ii） sufficient conditions for the existence of a positive solution of （CDI）e based on the Leray-Schauder＇s degree theory. Numerical simulations which support our theoretical analysis are also given.

Existence of spatiotemporal patterns in the reaction-diffusion predator-prey model incorporating prey refuge

The pattern formation in reaction-diffusion system has long been the subject of interest to the researchers in the domain of mathematical ecology because of its universal exis- tence and importance. The present investigation deals with a spatial dynamics of the Beddington-DeAngelis predator-prey model in the presence of a constant proportion of prey refuge. The model system representing boundary value problem under study is subjected to homogeneous Neumann boundary conditions. The asymptotic stability including the local and the global stability and the bifurcation as well of the unique pos- itive homogeneous steady state of the corresponding temporal model has been analyzed. The Turing instability region in two-parameter space and the condition of diffusion- driven instability of the spatiotemporal model are investigated. Based on the appro- priate numerical simulations, the present model dynamics in Turing space appears to get influenced by prey refuge while it exhibits diffusion-controlled pattern formation growth to spots, stripe-spot mixtures, labyrinthine, stripe-hole mixtures and holes repli- cation. The results obtained appear to enrich the findings of the model system under consideration.

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.

A reaction-diffusion model of forest boundary with seed dynamics

The density of forest cover based upon reaction diffusion model for mono-species of two age classes with seed dynamics is to be attempted. The prevailing densities of young, old species and airborne seedlings are resolved by homotopy perturbation method which is applied in reaction diffusion model. This model is utilized to verify the effect of the density of forest cover with the following variables namely seed reproduction, seed deposition, seed establishment rates, coefficients of aging of old tree and coefficients of mortality on the space variable.

A periodic reaction-diffusion system modelling man-environment-man epidemics

The purpose of this work is to study the spatial dynamics of a periodic reaction-diffusion epidemic model arising from the spread of oral-faecal transmitted diseases. We first show that the disease spreading speed is coincident with the minimal wave speed for monotone periodic travelling waves. Then we obtain a threshold result on the global attractivity of either zero or the positive periodic solution in a bounded spatial domain.

Explicit Traveling Wave Solutions to Nonlinear Evolution Equations

First of all,some technical tools are developed.Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.

The asymptotic stability model with for an SIQS epidemic diffusion

In this paper, an SIQS epidemic model with constant recruitment and standard inci- dence is investigated. Quarantine is taken into consideration on the basis of SIS model. The asymptotic stability of the equilibrium to a reaction^diffusion system with homo- geneous Neumann boundary conditions is considered. Sufficient conditions for the local and global asymptotic stability are given by linearization and the method of upper and lower solutions and its associated monotone iterations. The result shows that the disease-free equilibrium is globally asymptotically stable if the contact rate is small.