一类非经典反应扩散方程全局吸引子的正则性

考虑了一类非经典反应扩散方程全局吸引子的正则性。利用渐近先验估计证明了系统在H01(Ω)中的全局吸引子A1在D(A)中有界,并进一步获得A1即为系统在D(A)中的全局吸引子A2。     

一类反应扩散方程组解的渐近性质

我们对一类反应扩散方程组,通过构造上下解,证明了它的初边值问题解的存在性及唯一性.在此基础上,讨论了其平衡解的渐近稳定性及吸引区域.     

一类生物降解模型的解的渐近性

本文利用Ｌ＾ｐ估计，半群方法证明了一类产生于地下水生物降解模型的反应扩散方程组解的渐近性。     

一类非线性积分微分反应扩散方程的渐近解

研究了一类非线性积分———微分反应扩散方程.在适当的条件下,利用微分不等式理论,讨论了退化解具有两个交叉解的初值问题解的渐近性态.     

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。     

一类反应扩散方程解的熄灭现象

利用能量估计方法讨论了下述反应扩散方程的初边值问题解的渐近性态,分别给出解熄灭的充分条件和必要条件。这里λ>0,γ>0,β>0为常数,Ω?RN为有界域。文末给出说明文中方法处理高阶方程的例子。     

具有特殊扩散过程的反应扩散方程

本文考虑如下具有特殊扩散系数的化学反应扩散方程的整体解存在性、渐近性和局部解有限时间爆破,这里Ω是ＲＮ（Ｎ≥３）中的光滑有界区域,０∈Ω,１＜Ｐ＜Ｎ＋２／Ｎ－２．     

具有特殊扩散过程的反应扩散方程

本文考虑如下具有特殊扩散系数的化学反应扩散方程的整体解存在性、渐近性和局部解有限时间爆破,这里Ω是RN(N≥3)中的光滑有界区域,0∈Ω,1＜p＜N+2/N-2.     

一类反应扩散方程的行波解

1　引　　言由于反应扩散方程涉及的大量问题来自物理学、化学、生物学和人口动力学中众多的数学模型,因而有广阔的实际背景.其行波解引起了人们的兴趣,行波解是某个常微分方程的解,对某些传播速度,利用几何方法可以建立其解的存在性(见[1][2][3]).在文[4]中J.Canosa讨论了Fisher方程ut=2u2x+u(1-u)(1)行波解的存在性、逼近解和误差估计.所谓方程(1)的行波解是指形为u(x,t)=u(x-ct)=u(z)的解.众所周知,行波解u(x,t)=u(x-ct)=u(z)是方程(1)的行波解的充要条件是d2udz2+cdudz+u(1-u)=0(2)若u(z)是单调有界且不恒为常数,则u(z)叫做(1)的波前…     

一类带小参数反应——扩散型方程组的性态估计

得到了激光等离子能量交换模型研究中的一类反应－－扩散方程组的本解的存在性。并通过引进光滑符号函数对解析解的性态进行了估计,为数值方法的误差分析提供了理论依据。     

Dynamics of a Mutualistic Model with Diffusion

This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε_1+ ε_2 ≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε_1+ε_2= 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than 1(α_1α_2 1),while if the geometric mean of the interaction coefficients is less than 1(α_1α_2 1), there exists a global solution. Finally, numerical simulations are given.     

Asymptotic behavior of solutions for a class of predator-prey reaction-diffusion systems with time delays

The aim of this paper is to investigate the asymptotic behavior of solutions for a class of three-species predator-prey reaction-diffusion systems with time delays under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants of the reaction functions to ensure the convergence of the time-dependent solution to a constant steady-state solution. The conditions for the convergence are independent of diffusion coefficients and time delays, and the conclusions are directly applicable to the corresponding parabolic-ordinary differential system and to the corresponding system without time delays.     

Qualitative Properties of Saddle-Shaped Solutions to Bistable Diffusion Equations

We consider the elliptic equation ? Δu = f(u) in the whole ?^2m , where f is of bistable type. It is known that there exists a saddle-shaped solution in ?^2m . This is a solution which changes sign in ?^2m and vanishes only on the Simons cone 𝒞 = {(x ¹, x ²) ∈ ? ^m × ? ^m : |x ¹| = |x ²|}. It is also known that these solutions are unstable in dimensions 2 and 4.

In this article we establish that when 2m = 6 every saddle-shaped solution is unstable outside of every compact set and, as a consequence has infinite Morse index. For this we establish the asymptotic behavior of saddle-shaped solutions at infinity. Moreover we prove the existence of a minimal and a maximal saddle-shaped solutions and derive monotonicity properties for the maximal solution.

These results are relevant in connection with a conjecture of De Giorgi on 1D symmetry of certain solutions. Saddle-shaped solutions are the simplest candidates, besides 1D solutions, to be global minimizers in high dimensions, a property not yet established.     

A Reaction-diffusion System of a Prey with Three Genotypes and a Predator

The global existence and the asymptotic behavior of solutions to a reaction-diffusion system of a prey with three genotypes and a predator are considered. We establish the evolvement of a pure strain. Here an assumption concerning the diffusion is needed.     

一个具有可测数据的化学反应扩散系统

该文证明一个化学反应扩散系统当初始数据是有界非负犚犪犱狅狀测度时弱解整体存在,且给出了解收敛于正平衡解的充要条件．     

Fast Reaction Limit and Large Time Behavior of Solutions to a Nonlinear Model of Sulphation Phenomena

We investigate the qualitative behavior of solutions to the initial-boundary value problem on the half-line for a nonlinear system of parabolic equations, which arises to describe the evolution of the chemical reaction of sulphur dioxide with the surface of calcium carbonate stones. We show that, both in the fast reaction limit and for large times, the solutions of this problem are well described in terms of the solutions to a suitable one phase Stefan problem on the same domain.     

Asymptotic behavior of solutions of a three-species predator-prey model with diffusion and time delays

In this paper, we deal with a reaction-diffusion system with time delays arising from a three-species predator-prey model under the homogeneous Neumann boundary conditions, and study the asymptotic behavior of solutions.     

两参数反应扩散方程解的渐近性态

本文讨论了一类具有双参数的反应扩散方程初始边值问题.利用微分不等式理论,研究了初始边值问题解的渐近性态.     

一类具有扩散的互惠共食系统的存在性和全局吸引性

本文研究了两个互惠的捕食种群,其一具有饱和作用项,捕食同一食饵种群的反应扩散系统,通过构造上下解及单调序列,得到了该系统各类解的某些性质,其包括正静态解的存在性与全局吸引性,平凡解和半平凡解的稳定性与不稳定性等.