ASYMPTOTIC BEHAVIOR TOWARD THERAREFACTION WAVE FOR SOLUTIONS OFRATE-TYPE VISCOELASTIC SYSTEM WITH BOUNDARY EFFECT

1IntroductionWeconsiderthefollowinginitialboundaryvalueproblemonR =(o, oo)forarate-typeviscoelasticsystemwiththeinitial-boundaryconditionsWherev5uand-pdenotethestrain,partialvelocityandstressrespectively,whileEisapositiveconstant,whichrepresentthedynamicYoung'smodulus,andT>Oisarelaxationtime.Forsimplicity,weassumeT=1.PR(v)standsfortheequilibriumvalueforp-Theinitialdata(vo,bolpo)(x)areassumedtotendtotheconstantstate,asx- oowherep =pR(v )sincepR(v)istheequilibriumvaluef0rp.M0reover,thecompa…     

ASYMPTOTIC BEHAVIOR AND EXISTENCE OF POSITIVE SOLUTIONS FOR A NEUTRAL DIFFERENCE EQUATION

１ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｅｕｔｒａｌｄｉｆｅｒｅｎｃｅｅｑｕａｔｉｏｎ△（ｘｎ－ｃｘｎ－ｍ）＋ｐｎｘｎ－ｋ＝０，ｎ＝Ｎ，Ｎ＋１，Ｎ＋２，…，（１）ｗｈｅｒｅｃａｎｄｐｎａｒｅｒｅａｌｎｕｍｂｅｒｓ，ｋ，ｍａｒｅｐｏｓｉｔｉｖ...     

一个燃烧波模型解的存在唯一性与渐近行为

本文讨论一类燃烧波模型.在较弱的条件下证明该问题解的存在唯一性,并给出了解的渐近行为.     

一类带反应项的多种群趋化性模型解的性态(英文)

本文研究了一类带反应的多种群趋化性Othmer-Stevens模型的问题,利用抛物方程上下解和迭代的方法,获得了该模型在不同条件下的解的爆破,熄灭等渐进性态,推广了单种群模型的结果。     

BEHAVIOR OF SOLUTIONS FOR A MODEL IN HETEROGENEOUS CATALYTIC REACTION-DIFFUSION

1IntroductionHereweinvestigatethefollowing:irreversiblemodelinthekineticsofhete-rogeneouscatalyticreaction-diffusion:where0ncRNisaboundeddomainwithsmoothboundaryafl,kden0tedtheouternormalderivationon0n,uandvrepresenttheconcentrati0ns0ftworeactants,c0nstan…     

带Neumann边界条件的相场方程解的渐近性态

利用Simon-Lojasiewicz型不等式,获得了带Neumann边界条件的相场方程解的渐近性态.本文所考虑的稳态问题含有非局部项.     

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR THE 3D COMPRESSIBLE NON–ISENTROPIC EULER EQUATIONS WITH DAMPING

We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.     

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF STRONGLY NONLINEAR NON-AUTONOMOUS EQUATION

In this paper, using the singularly perturbed theory and the boundary layer corrective method, the asymptotic behavior of solution for a class of strongly nonlinear non-autonomous equations and the infection for asymptotic behavior of the solution with regard to the boundary condition are studied. According to the different regions of the boundary value, the asymptotic expansions of the solution for the original problem are obtained simply and conveniently.     

ASYMPTOTIC BEHAVIOR OF SINGULARLY PERTURBED SOLUTION FOR A CLASS OF ROBIN PROBLEM OF NONLINEAR NON-AUTONOMOUS EQUATION

In this paper, using the layer theory, a class of singularly perturbed Robin problem of nonlinear non-autonomous equation is considered. According to the different regions of the boundary value, the asymptotic behaviors of solution for the original problem are obtained simply and conveniently.     

ASYMPTOTIC BEHMIOUR IN A REACTION-DIFFUSION SYSTEM

1IntroductionInrecentyearslinordertoremovethecontalltinantsillundergroundwater,lllanyscielltistspaymoreandmoreattentiontothewayofmicroorganislllandsetupthefollowillRIn.d.l[1]whereSrepresentsthemasscollcentratiolloftheprimarysubstrate,tistillle,l):istheaveragelineargrollndwatervelocity,D;isthehydrodynamicdispersiollcoefficient,Aisthelllassconcentrationoftheelectronacceptor,Msisthemicrobialmassconcentratiollillsolutioll,Mtisthetotalactivendcrobialbiomassconcentrationalld7'istilefirstordernlicr…     

Lié nard 方程解的有界性与整体渐近性

本文研究Lienard方程x＋f（x）x＋g（x）＝e（t）的解的有界性及整体渐近性态,并获得了所有解及它们的导数有界与收敛于零的充要条件．     

GLOBAL EXISTENCE OF SMOOTH SOLUTION FOR BOLTZMANN-POISSON SYSTEM WITH SMALL DATA

1IntroductionThebasicequationinsemiconductorkinetictheoryistheBoItzmannEquation.Iftherelevantphysicsconstantsaretakenasone,theBoltzmannEquationin3D,undertheattractforce,canbewrittenas:o,f vV.f-E.V.f=Q(f),xER',vER',t>o,(1.1)wheref(t,x,v)isadistributionfunction,itrepresentsthefractionofoccupiedstatesattimetE[o,oo),atthepoint(x,v)eR'xR3oftheposition-velocityspace.E(f,x)ER'istheelectricfield-IfthepotentialcorrespondingtotheelectricfieldE(f,x)isdenotedbyV(t,x),thenAndV(t,x)satisfiesthePoi…     

PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.     

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A SINGULAR PARABOLIC EQUATION

In this paper,we study the initial-boundary value problem for a class of singular parabolic equations.Under some conditions,we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regularization method and the sub-super solutions method.As a byproduct,we prove the existence of solutions to some problems with gradient terms,which blow up on the boundary.     

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE NONLINEAR HEAT-CONDUCTION EQUATION AND ITS APPLICATION

1 IntroductionIn the heat-conduction equationp is the density,c is the specific heat,k is the thermal conductivityLet u = w -- wco be therelative temperature, where woo is the environmental temperature. In many cases, the thermalconductivity k is dependent of the temperature,forrexample, the heat-conduction of electron iuthe plasma body and the radiation heat-conduction in the high temperature,k(u) = uoum--' (m > 1).Assume that p, c are constants, then the equation (1.1) can be written asWe c…     

ASYMPTOTIC BEHAVIOR OF SOLUTION BRANCHES OF NONLOCAL BOUNDARY VALUE PROBLEMS

In this article, by employing an oscillatory condition on the nonlinear term,a result is proved for the existence of connected component of solutions set of a nonlocal boundary value problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence of infinitely many solutions of the nonlinear problem for all parameter values in that interval.     

THE DECAY BEHAVIOR OF SOLUTIONS FOR NONLOCAL BOUNDARY PROBLEMS

A parabolic equation defined on a bounded domain with boundary condition being nonlocal is considered. The existence and the dynamic behavior of the solutions for linear and semilinear equations are investigated in special spaces. One will find that the behavior of the solutions are affected by the boundary conditions. A semigroup approach is employed in this paper.     

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR A NONLINEAR ELLIPTIC EQUATION ARISING IN ASTROPHYSICS

The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -△u=φ(r)up-1,u>0 in RN, u ∈ D1,2(RN),where N≥ 3,x = (x',z)∈ RK×RN-K,2≤K≤N,r =|x'|.It is proved that for 2(N -s)/(N-2) < p < 2* = 2N/(N -2),0 < s < 2, the above equation has a ground state solution and a cylindrically symmetric solution. For p=2*, the above equation does not have a ground state solution but a cylindrically symmetric-solution, and when p close to 2*, the ground state solutions are not cylindrically symmetric. On the other hand, it is proved that as p close to 2*, the ground state solution up has a unique maximum point xp = (x'p,zp) and as p→2*, |x'p|→r0 which attains the maximum of φ on RN.The asymptotic behavior of ground state solution up is also given, which also deduces that the ground state solution is not cylindrically symmetric as p goes to 2*.     

一类具有无穷时滞的Logistic方程的正概周期解存在性与渐近性

利用李雅普诺夫泛函解决了George Seifert在1996年所提公开问题.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR A CLASS OF DELAY DIFFERENCE EQUATION

We propose a class of delay difference equation with piecewise constant nonlinearity. Such a delay difference equation can be regarded as the discrete analog of a differential equation. The convergence of solutions and the existence of asymptotically stable periodic solutions are investigated for such a class of difference equation.