退化的半线性反应扩散方程组解的熄灭

In this paper,the initial boundary value problem of semilinear degenerate reaction-diffusion systems is studied.The regularization method and upper and lower solutions technique are employed to show the existence and continuation of a positive classical solution.The location of quenching points is found.The critical length is estimated by the eigenvalue method.     

Reaction-diffusion waves in coupled isothermal autocatalytic chemical systems

The initiation and propagation of reaction-diffusion travellingwaves in two regions, coupled together by a linear diffusiveinterchange across a semipermeable membrane is considered. Twosystems are considered in detail where there are two chemicalspecies present, species A and the autocatalytic species B.The first system is governed by quadratic autocatalysis in bothregions together with a linear decay of the autocatalyst inonly one region, with the coupling taken to be via the exchangeof species A. The second system has the reaction scheme of cubicautocatalysis and linear decay of the autocatalytic speciesB in region I, while region II is taken to be chemically inertcontaining only species A, with the mode of coupling betweenthe two regions again being via A. These two systems are consideredvia an initial-value problem in which the amounts of the autocatalystare introduced locally into a uniform concentration of speciesA. A priori bounds for the initial-value problem are first obtained,and then conditions for the initiation of travelling waves forsmall initial inputs of the autocatalyst are derived. Theseresults are extended for the first system to all initial inputsof the autocatalyst. The effects of strong coupling are thenexamined. Numerical results are presented to demonstrate theeffects of varying the parameters of the two systems as predictedby our analysis. Finally, the authors examine the equationsgoverning the permanent-form travelling waves and derive generalproperties of their solution together with a solution for weakcoupling.     

Reaction-diffusion front speed enhancement by flows

We study flow-induced enhancement of the speed of pulsating traveling fronts for reaction-diffusion equations, and quenching of reaction by fluid flows. We prove, for periodic flows in two dimensions and any combustion-type reaction, that the front speed is proportional to the square root of the (homogenized) effective diffusivity of the flow. We show that this result does not hold in three and more dimensions. We also prove conjectures from Audoly, Berestycki and Pomeau (2000) [1], Berestycki (2003) [3], Fannjiang, Kiselev and Ryzhik (2006) [11] for cellular flows, concerning the rate of speed-up of fronts and the minimal flow amplitude necessary to quench solutions with initial data of a fixed (large) size.     

Travelling Wave Front Solutions for Reaction-diffusion Systems

In this paper by using upper-lower solution method, under appropriate assumptions on f and g the existence of travelling wave front solutions for the following reaction-diffusion system is proved: {u_t - u_{xx}, = f(u,v) v_t - v_{xx} = g(u, v) As an application, the necessary and sufficient condition of the existence of monotone solutions for the boundary value problem {u" + cu' + u(1 - u- rv) = 0 v" + cv' - buv = 0 u(-∞) = v(+∞) = 0 u(+∞) = v(-∞) = 1 where 0 < r < 1, 0 < b < \frac{1 - r}{r} are known constants and c is unknown constant to be obtained.     

Stochastic Reaction-diffusion Equations Driven by Jump Processes

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.     

技术创新的反应扩散模型研究

首先利用微分方程来描述技术创新的反应扩散过程，在充分考虑技术与环境之间相互关系的基础上，给出了具有代表性的几种技术创新扩散模型：竞争、互补、替代等模型；再根据微分方程定性理论，对所建立的模型进行经济分析，以寻求技术与环境之间的最佳协调状态。为模拟与预测市场的新旧技术更替及结构演变过程提供了理论依据，同时对技术创新的发展完善及创新技术的扩散推广具有一定的现实意义。     

一类非局部反应扩散方程组解的爆破性质

该文研究一类带非局部源项的反应扩散方程组. 作者证明了初值充分大时解在有限时刻爆破, 建立了爆破解的爆破速率估计以及边界层估计.     

一类反应扩散方程解的渐近性质及其应用

本文讨论问题 ｕｔ＝Ａｕｘｘ＋ｆ（ｘ，ｔ，ｕ）， ｕｘ｜ｘ＝０＝０，ｕｘ｜ｘ＝１＝０， ｕ｜ｔ＝０＝ｕ０（ｘ）。 的解的渐近性质，将参考文献［１］的Ｌ＾２范数估计     

Reaction-diffusion models from the Fokker-Planck formulation ofchemical processes

A Fokker-Planck-type model is proposed to describe the kineticsof certain chemical reactions. In particular, the competitionbetween transport and reaction processes is analysed. The studyis carried out considering various scalings of interaction,measured by the exponent of a small parameter related to themean free path. In the most significant case of competitionbetween both effects, the lowest-order density in the asymptoticexpansion obeys a reaction-diffusion equation. Such an equationwas earlier considered as the starting point in the study ofthese processes by other authors (e.g. by Schlgl). For otherinteraction scalings, the prevalence of chemical processes impliesthat the lowest-order density is determined by the (algebraic)equations of chemical equilibrium. In contrast, when transportprevails, the reaction terms affect only higher-orderdensities.     

一类反应扩散系统的不同时爆破临界指标(英文)

本文讨论了一类反应扩散方程组齐次第一初边值问题u_t=△u+u~mv~p,v_t=△v+u~qv~n的不同时爆破临界指标问题.在一定初值条件下,本文给出了径向解的四种同时、不同时爆破现象:存在初值使得同时爆破或不同时爆破发生;任何爆破均是同时或不同时的.通过对指标参数的完整分类给出了四种爆破现象的充分必要条件,并且得到了解的全部爆破速率估计.所得结果推广了以前的相应工作.     

一类反应扩散方程的分歧分析

文章讨论了一类反应扩散方程的分歧（分岔）现象。运用所谓基于Ｌ－Ｓ（李雅普诺夫－施密特）约化的奇异理论方法,得到了满意的结果。     

A Finite Element Method for Singularly Perturbed Reaction—diffusion Problems

A finite element method is proposed for the sing ularly perturbed reaction-diffusion problem.An optimal error bound is derived,independent of the perturbation parameter.     

Steady-state Solution for Reaction-diffusion Models with Mixed Boundary Conditions

In this paper, we deal with a diffusive predator-prey model with mixed boundary conditions, in which the prey population can escape from the boundary of the domain while predator population can only live in this area and can not leave. We first investigate the asymptotic behaviour of positive solutions and obtain a necessary condition ensuring the existence of positive steady state solutions. Next, we investigate the existence of positive steady state solutions by using maximum principle, the fixed point index theory, Lpestimation, and embedding theorems, Finally, local stability and uniqueness are obtained by linear stability theory and perturbation theory of linear operators.     

一类反应扩散方程组的渐近行为

本文讨论了一类反应扩散方程组的渐进行为,证明了对任意ｕ〉０解在Ｃ＾ｖ（Ω）中收敛于常数平衡解,并推广了以往的结论。     

非局部时滞Schoner竞争反应扩散方程的行波解

构造并研究了一类具有非局部时滞Schoner竞争反应扩散模型．每一个种群的成熟期是一个常数,而且只有成年种群存在竞争,幼年的种群并不存在竞争,此外种群个体在空间区域中的运动是随机行走的．我们利用Wang,Li和Ruan建立的具有非局部时滞的反应扩散系统的波前解存在性理论,证明了连接两个边界平衡解的行波解的存在性．     

反应扩散系统双稳波前解的全局渐近稳定性

该文研究一类拟单调反应扩散系统的古典解的渐近行为.在双稳的假定下,利用上、下解方法和单调半流的收敛性结果,证明了当系统的初值在±∞处的极限分别"大于"和"小于"其中间平衡点时,初值问题的解收敛于一个连接两个稳定平衡点的波前解.最后,将结果应用到一个传染病模型.     

On Time-space Fractional Reaction-diffusion Equations with Nonlocal Initial Conditions

This paper investigates the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. Based on the operator semigroup theory, we transform the time-space fractional reaction-diffusion equation into an abstract evolution equation. The existence and uniqueness of mild solution to the reaction-diffusion equation are obtained by solving the abstract evolution equation. Finally, we verify the Mittag-Leffler-Ulam stabilities of the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. The results in this paper improve and extend some related conclusions to this topic.     

具有Hamilton结构的反应扩散方程组的整体吸引子

本文研究了具有Hanmilton结构的反应扩散方程组,证明其存在不变区域及吸引集,再证明其整体吸引子的存在性。