1.

QUENCHING PROBLEMS OF DEGENERATE FUNCTIONAL REACTIONDIFFUSION EQUATION





Ma Zhongtai 《Annals of Differential Equations》,2006年第3期


This paper is concerned with the quenching problem of a degenerate functional reactiondiffusion equation. The quenching problem and global existence of solution for the reactiondiffusion equation are derived and, some results of the positive steady state solutions for functional elliptic boundary value are also presented.

2.

ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF REACTION DIFFUSION EQUATIONS





MoJiaqi LinWantao ZhuJiang《高校应用数学学报(英文版)》,2004年第19卷第4期


A class of initial boundary value problems for the reaction diffusion equations are considered. The asymptotic behavior of solution for the problem is obtained using the theory of differential inequality.

3.

LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION





罗操《数学物理学报(B辑英文版)》,2013年第33卷第1期


The paper is concerned with the longtime behaviour of the travelling fronts of the damped wave equation αutt+ut=uxx V’(u) on R.The longtime asymptotics of the solutions of this equation are quite similar to those of the corresponding reactiondiffusion equation ut=uxxV’(u).Whereas a lot is known about the local stability of travelling fronts in parabolic systems,for the hyperbolic equations it is only briefly discussed when the potential V is of bistable type.However,for the combustion or monostable type of V,the problem is much more complicated.In this paper,a local stability result for travelling fronts of this equation with combustion type of nonlinearity is established.And then,the result is extended to the damped wave equation with a case of monostable pushed front.

4.

THE NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH TIME DELAY 被引次数：7





莫嘉琪 冯茂春《数学物理学报(B辑英文版)》,2001年第2期


Mo studied a class of singularly perturbed problems for reaction diffusion equations in[4][8]. Now we consider the following nonlinear singularly perturbed prob1em with time delaywhere i = 1, 2,' l N, u = (u1, u2l', UN), u* = (u1, u;,', uX) and u: == ui(t  er, xt e) (thereis similar notation of the superscript k*" below), rt e are positive C..,tant. and re is the timedelay, andz = (xl, xzl... l z.) E O, fl denotes a boullded region in R", 0fl signifies a boundary of fl forclass C' …

5.

A Nonlinear Singularly Perturbed Problem for Reaction Diffusion Equations with Boundary Perturbation





JiaqiMo WantaoLin《应用数学学报(英文版)》,2005年第21卷第1期


A nonlinear singularly perturbed problems for reaction diffusion equation with boundary perturbation is considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems of reaction diffusion equations is studied using the theory of differential inequalities.

6.

Infinitely Many Signchanging Solutions for a Schrdinger Equation in R~N





洪明理 李永青《数学进展》,2006年第6期


We consider the existence of infinitely many signchanging solutions for the nonlinear timeindependent schrodinger equations of the form where Vλ(x) =λa(x) 1. This problem originates from various problems in physics and mathematical physics. In constructive field theory, (1.1) is called a nonlinear Euclidean scalar field equation. In chemical dynamics, a solution of (1.1) is a stationary state of the reaction diffusion equation

7.

ON NONLINEAR COUPLED REACTIONDIFFUSION SYSTEMS





梅茗《数学物理学报(B辑英文版)》,1989年第2期


In this paper, the problem of initial boundary value for nonlinear coupled reactiondiffusion systems arising in biochemistry, engineering and combustion_theory is considered.

8.

POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE pLAPLACIAN EQUATIONS





Leszek GASINSKI Nikolaos S. PAPA GEORGIOU《数学物理学报(B辑英文版)》,2014年第3期


We consider a parametric Dirichlet problem driven by the pLaplacian with a Caratheodory reaction of equidiffusive type. Our hypotheses incorporate as a special case the equidiffusive plogistic equation. We show that if λ1 〉 0 is the principal eigenvalue of the Dirichlet negative pLaplacian and ）λ 〉 λ1 （/k being the parameter）, the problem has a unique positive solution, while for ）λ ∈ （0, λ1], the problem has no positive solution.

9.

THE EXISTENCE AND THE NONEXISTENCE OF GLOBAL SOLUTIONS OF A FREE BOUNDARY PROBLEM





YinRong YuWanghui《偏微分方程(英文版)》,2004年第17卷第2期


We study a free boundary problem of parabolic equations with a positive parameter τ included in the coefficient of the derivative with respect to the time variable t. This problem arises from some reactiondiffusion system. We prove that, if τ is large enough, the solution exists for 0<t<+∞;while, if τ is small enough, the solution exists only in finite time.

10.

A CLASS OF NONLINEAR SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH BOUNDARY PERTURBATION





Mo Jiaqi《高校应用数学学报(英文版)》,2007年第22卷第2期


A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.

11.

THE CORNER LAYER SOLUTION TO ROBIN PROBLEM FOR REACTION DIFFUSION EQUATION





Lihua Chen Dept. of Math. and Computer Science Fuqing Branch of Fujian Normal University Fuqing Fujian Zhaohui Wen Institute of Applied Math.《Annals of Differential Equations》,2012年第2期


A class of Robin boundary value problem for reaction diffusion equation is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the corner layer solution to the initial boundary value problem are studied.

12.

催化反应中的一类奇摄动边值问题





史少云《东北数学》,2000年第16卷第3期


§1. Introduction We are concered with the singularly perturbed boundary value problemε2y″=y3,(1)y(0)=1, y(1)=2,(2)where ε＞0 is a positive small parameter. This problem arises as models for certain catalytic reactions in chemical engineering. The study of that problem has been paid much attention for the boundary layers of the problem exihibit the behavior of nonexponential decay. There have been some works on this subject ［1］［4］. In particular, Howes and Chang［1］ gave an accurate…

13.

A CLASS OF SINGULARLY PERTURBED INITIAL BOUNDARY PROBLEM FOR REACTION DIFFUSION EQUATION





XieFeng《分析论及其应用》,2003年第19卷第1期


The singularly perturbed initial boundary value problem for a class of reaction diffusion equation is considered. Under appropriate conditions, the existenceuniqueness and the asymptotic behavior of the solution are showed by using the fixedpoint theorem.

14.

Analysis of a Preypredator Model with Disease in Prey





Li Jianjun Gao Wenjie Sun Peng《东北数学》,2010年第26卷第1期


In this paper, a system of reactiondiffusion equations arising in ecoepidemiological systems is investigated. The equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases. Local stability of the constant positive solution is considered. A number of existence and nonexistence results about the nonconstant steady states of a reaction diffusion system are given. It is proved that if the diffusion coefficient of the prey with disease is treated as a bifurcation parameter, nonconstant positive steadystate solutions may bifurcate from the constant steadystate solution under some conditions.

15.

ASYMPTOTIC SOLUTION FOR A CLASS OF WEAKLY NONLINEAR SINGULARLY PERTURBED REACTION DIFFUSION EQUATION





Mo Jiaqi 《Annals of Differential Equations》,2006年第22卷第4期


In this paper a class of nonlinear reaction diffusion problems are considered. Using the perturbed method, the asymptotic solution for corresponding problem is obtained.

16.

SINGULAR PERTURBATION OF NONLINEAR BOUNDARY VALUE PROBLEMS





章国华 林宗池《应用数学和力学(英文版)》,1984年第5卷第5期


In this paper we consider the boundary value problem where ε.μ are two positive parameters. Under f_y≤k<0 and other suitable restrictions, there exists a solution and it satisfied where y_(0,0)(x) is solution of reduced problem while y_ij,j(x)(j=0,1,...,i;i=1,2,...,m) can be obtained successively from certain linear equations.

17.

A note on a diffusive predatorprey model and its steadystate system





Rui Peng Ming Xin Wang Guo Ying Yang《数学学报(英文版)》,2010年第26卷第5期


In this note, a diffusive predatorprey model subject to the homogeneous Neumann bound ary condition is investigated and some qualitative analysis of solutions to this reactiondiffusion system and its corresponding steadystate problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some nonexistence results for nonconstant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.

18.

SEMIDISCRETIZATION IN SPACE OF NONLINEAR DEGENERATE MRABOLIC EQUATIONS WITH BLOWUP OF THE SOLUTIONS





Tetsuya Ishiwata 《计算数学(英文版)》,2000年第6期


1. IntroductionLet n be a bounded domain in AN with smooth boundary Off. We consider thefollowing initial boundary value problem:where 6, p are positive constants and "o(x) is a nonnegative bounded continuous function on fi.When N = 1 and 5 ~ 2, the problem arises in a model for the resistive diffusion of aforcefree magnetic field in a plasma confined between two walls in one dimension (see[5], [8], [9], [10] and [14]). Equation (1) also describes the evolution of the curvatureof a locally…

19.

THE EXISTENCE OF SOLUTION OF A CLASS OF TWOORDER QUASILINEAR BOUNDARY VALUE PROBLEM





何清 冀春慈《应用数学和力学(英文版)》,1992年第13卷第10期


Ref. [1] discussed the existence of positive solutions of quasilinear twopoint boundary problems: but it restricts O

20.

Singularly perturbed solution to semilinear reaction diffusion equations with two parameters





莫嘉琪 刘树德《应用数学和力学(英文版)》,2009年第30卷第5期


A class of singularly perturbed initial boundary value problems for semilinear reaction diffusion equations with two parameters is considered, Under suitable conditions and using the theory of differential inequalities, the existence and the asymptotic behavior of the solution to the initial boundary value problem are studied.
