A PRIORI BOUNDS FOR GLOBAL SOLUTIONS OF HIGHER-ORDER SEMILINEAR PARABOLIC PROBLEMS

In this paper, we derive a priori bounds for global solutions of 2m-th order semilinear parabolic equations with superlinear and subcritical growth conditions. The proof is obtained by a bootstrap argument and maximal regularity estimates. If n≥ 10/3m, we also give another proof which does not use maximal regularity estimates.     

一类四阶非线性波动方程解的爆破与衰减

本文研究了非线性阻尼项与源项的竞争对具有强阻尼项的四阶波动方程解的影响.利用不动点原理和势井方法给出了方程局部弱解存在唯一性满足的条件,证明了当mp且初始能量E(0)0时,解将在有限时间内爆破.同时对m,p的大小关系不加任何限制但存在t_0使0E(t_0)d的情况下,利用稳定集,研究了整体解的存在性,并得到了解的能量衰减估计.最后借助修正的能量泛函,指出当m≥p时弱解也是整体存在的,推广并改进了文献[1-6]中的结果.     

关于一类非线性发展方程整体解的存在性问题

本文研究一类模拟非线性弹性杆的纵振动的非线性发展方程的初边值问题，证明了其整体解的存在性、唯一性、光滑性及在一定条件下，整体解的不存在性。     

H~1 SOLUTIONS FOR A CLASS OF SEMILINEAR PARABOLIC SYSTEMS

1IntroductionInthispapertweconsiderthefollowingsystemswithinitialvaluewhereu=(tLt,'',Wi),F=(FI,'.',Fn),t20,--co0,thereisasolutionu(x,f)of(1.1),suchthatIIullHI5C(T).C(T)isaconstantdependingboundlyon"o(z)andT.Ifb=0,then(1.l)isthetypicalselnilinearheatsystems,i.e.therearemugpapersdealingwiththesystems(1.3).Theinvestigationill…     

THE GLOBAL DUFORT-FRANKEL DIFFERENCE APPROXIMATION FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

1.IntroductionInthispaperweconsiderthefollowinginitial-valueproblemofnonlinearreactiondiffusionequation:HerefiisaboundeddomaininRd(d<3)withaLipschitzboundaryOffand7isapositiveconstallt.Lettheset{in*l:j(u*)=0}benotemptyandu=ma-c{lu*I:f(u*)=0}.Assumptionont…     

GLOBAL EXISTENCE OF SOLUTIONS FOR A STRONGLY COUPLED REACTION-DIFFUSION SYSTEM

1IntroductionInthispaper,weinvestigatetheglobalexistencealldtllliqllellessofthesmoothsolutiolltotilefollowingIBVPHerefiCR'1isaboulldeddomainwithsllloothboundaryoff,alldal,uZarcunkllowllfullctiolls,QT=(0,T)xfi,ST=(0,T)xoff,Tisanarbitrarypositiveconstallt,R=(--co, co).BI.'Itk=orb(f,x:)% aam(t,x)'(Lk,kistheoutwardnormalderivative,AistheLaplacianoperator,7t(k=(%,....%)(k=1,2)arethegradients.nisanarbitrarypositiveinteger.IBVP(1.1)coillesfi.ommanymathematicalalldphysicalproblelll.Ill11],fo…     

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.     

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

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

具非线性非局部边界条件的一类多孔介质方程解的整体存在与爆破

本文研究了具有非线性非局部边界条件的一类退化型多孔介质方程.利用比较原理和上下解的方法,获得了方程的解是否在有限时刻爆破或整体存在的准则,这些结果表明,权重函数g(x,y)及指数l的大小对于问题解的爆破与否起着关键的作用.最后研究了爆破解的爆破率.     

ON THE RATE OF CONVERGENCE OF SOLUTIONS FOR A CLASS OF DIFFERENCE EQUATIONS

1IntroductionConsiderthefollowingdifferenceequationwhereGfRxR-Riscontinuous,p:Z -R ,k;Z -Z ,p(n)5M,k(n)5k,MER ,kEZ ;ZandZ denotethesetsofintegersandnonnegativeintegers,respective1y.Forintegersaand5,a>6,wedefineZ(a,5)={a,a l,'',6},Z(a)={a,a l,'.}.Weassumethat(i)G(x,.)ismonotonenon-decreasing,(ii)G(.,y)ismonotonenon-increasing;(iii)G(x,x)=o,G(x,y)5oforx>yandG(x,y)2oforx相似文献   

一类非线性三阶三点边值问题的解和正解

考察了一类含有一阶和二阶导数的非线性三阶三点边值问题的解和正解.通过构造适当的Banach空间并且利用相应的积分方程建立了两个存在定理.主要结论表明,只要非线性项在其定义域的某个子集上的"高度"是适当的,该问题存在一个解或者正解.     

A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate of.the iteration.     

奇异半线性非局部反应扩散方程Cauchy问题局部解的存在性

本文讨论如下初值问题局部解的存在性 u/ t- (1/ tσ)Δu =(∫RNuλ(t,y) dy) p /λur + f (x) ,t>0 ,x∈ RNlimt→ 0 + u(t,x ) =0 ,　　　　　　　　　　　　　 x∈ RN其中σ>0 ,λ≥ 1,p≥ 0 ,r≥ 1,p+ r>1,f (x)连续有界非负但不恒等于零 ,Δ是 N维 L aplace算子 ,所得结论推广了文献 [2 ,3]的相应结果     

GLOBAL STRONG SOLUTIONS FOR A CLASS OF BBM-BO TYPE EQUATION

1IntroductionBBMequatiollbut box~'uxxt=0,x6R,t>0,(l.1)isderivedinnonlineardispersivesystemsbyT.B.Benjamin,J.H.L.BonaandJ.J.Mahony'asamodelequationforlongwaves.TheypointedoutthatthismodelismoresuitabletoreplaceKDVequation(see[2],[4]).BOequationILt 2'UU. HU.:.=0,XER,t>0,(1.2)arisesinthestudyoflollginternalgravitywavesilldeepstrafiedfluids(see[51,[9]).Bothofthelllarewell-kllownandhavebeenwidelystudied(see[31,[10],[11],[12]).Inthispaper,wecollsiderthefollowingBBM-BOtypeequationwithini…     

一类多维非线性反应扩散方程有限差分格式的稳定性问题(英文)

本文研究了一类多维线性反应扩散方程差分格式的稳定性.利用量未知元方法,建立了具有增量未知元的有限差分格式;然后利用非线性Galerkin方法,得到该差分格式的稳定性条件.通过对该格式的稳定性分析,说明和经典的差分格式的稳定性相比较,带有增量未知元的有限差分格式的稳定性得到了提高.     

BLOW-UP RATE OF SOLUTIONS FOR P-LAPLACIAN EQUATION

In this note we consider the blow-up rate of solutions for p-Laplacian equation with nonlinear source, ut = div（｜↓△u｜p-2↓△u）＋uq, （x, t） ∈ RN × （0, T）, N ≥ 1. When q 〉 p - 1, the blow-up rate of solutions is studied.     

A PRIORI AND A POSTERIORI ERROR ESTIMATES OF A WEAKLY OVER-PENALIZED INTERIOR PENALTY METHOD FOR NON-SELF-ADJOINT AND INDEFINITE PROBLEMS

In this paper, we study a weakly over-penalized interior penalty method for non-self- adjoint and indefinite problems. An optimal a priori error estimate in the energy norm is derived. In addition, we introduce a residual-based a posteriori error estimator, which is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to validate our theoretical analysis.     

一类非线性p-Laplace边值问题的正解

应用锥理论和不动点指数方法,在与相应齐次增算子的第一特征值相关的条件下,得到了下述非线性p-Laplace边值问题{(|u″|p-1u″)"=f(t,u),t∈(0,1),u(0)=u(1)=u″(0)=u″(1)=0的正解,改进了相关文献中的结论     

一类二阶非线性微分方程解的全局二分行为

本文讨论非周期二阶非线性微分方程：x“=f(t，x，x‘)解的全局二分行为，所得结果较好地改进和推广了关于周期方程的相应工作．