一类具交错扩散的强耦合退化抛物方程组解的整体存在与非存在性

本文研究了一类具交错扩散的强耦合拟线性退化抛物方程组初边值问题正古典解的局部存在,整体存在与非整体存在性.利用正则化方法和先验估计技巧证明了该问题正古典解的局部存在性,并且分别给出了该问题是否存在整体古典解的充分条件.结果表明当种群内竞争强于种群间互惠作用时,此问题存在整体解;而当两种群具有强互惠作用时,所有解都是非整体的.     

一类非经典扩散方程整体解的存在唯一性及长时间行为

本文讨论非经典扩散方程第一初边值问题整体解的存在唯一性及长时间行为，建立了一系列新的结果，较好地改进许多已有的结论．     

THE CAUCHY PROBLEM FOR A CLASS OF DOUBLY DEGENERATE NONLINEAR PARABOLIC EQUATION

This article studies the Cauchy problem for a class of doubly nonlinear degenerate parabolic equations . Under certain conditions, the author considers its regularized problem and establishes some estimates. On the basis of the estimates, the existence and uniqueness of the generalized solutions in BV space are proved.     

ON GLOBAL EXISTENCE AND NONEXISTENCE FOR SOME NONLINEAR PARABOLIC EQUATIONS

0IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblemforthefailliliarequationwherefiisaboundeddomaininR\"withsmoothboulldaryoff,p22isacollstantalldlp(z,u)l5of'(tl\" 'forsomea20andc>0.FOrp(x,ti)=Itll\"'u,theauthorsofpaper[4,7llolwereillterestedillllollllegativesolutionandhadobtainedfollowillgresults(alsosee[12]).1)If25a 2相似文献   

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.     

SOME RESULTS ON A DEGENERATE AND SINGULAR DIFFUSION EQUATION

In this article,a degenerate and singular diffusion problem is studied.The ex- istence of solutions is established by parabolic regularization.Some properties of solutions, for instance,asymptotic behavior,are also discussed.     

EXISTENCE OF WEAK SOLUTIONS FOR A DEGENERATE GENERALIZED BURGERS EQUATION WITH LARGE INITIAL DATA

11MroduCtlonIn this paper we will investigate the global exlstence ofwe欢 solutions to a de欧nerate辟nerajlzed Bur驴d equatllJll in the formut ＋(。侧。＝t。。。,x E R‘,t＞0(1．1)with the initial data刚,x)一。。卜 卜)(1．1)is not only a means to study hxPerbolic conser、nonl。s[1,2]but also the mathematicalmodel of*the*、 propapatlon offinlt。。plltude sound w。es in、i劝l。area ofduct(see[3;4]),where u is an roustlc vrable,with the linear effects of chang6s!n the duct area taken out;andt I…     

GLOBAL EXISTENCE FOR A PARTICULAR INHOMOGENEOUSCONVECTION DIFFUSION SYSTEM

ＧＬＯＢＡＬＥＸＩＳＴＥＮＣＥＦＯＲＡＰＡＲＴＩＣＵＬＡＲＩＮＨＯＭＯＧＥＮＥＯＵＳＣＯＮＶＥＣＴＩＯＮＤＩＦＦＵＳＩＯＮＳＹＳＴＥＭＺｈｕＣｈａｎｇｊｉａｎｇ（朱长江）ＺｈａｏＨｕｌｊｉａｎｇ（赵会江）（ＹｏｕｎｇＳｃｉｅｎｔｉｓｔＬａｂｏｒａｔｏ...     

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC EQUATIONS IN EXTERIOR DOMAINS

This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = (σ+m)n/(n-σ-2) is its critical exponent provided max{-1, [(1-m)n-2]/(n+1)} σ n-2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Furthermore, we demonstrate that if max{1, σ + m} p ≤ pc, then every positive solution of the equations blows up in finite time; whereas for ppc, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n ≤σ+2.     

EXTINCTION AND GLOBAL ATTRACTIVITY TO A NONLINEAR DISCRETE TWO SPECIES COMPETITIVE SYSTEM

In this paper, a nonlinear discrete two species competitive system is considered. Sufficient conditions which guarantee that one of components is driven to extinction while the other is globally attractive are obtained.     

GLOBAL ATTRACTOR FOR CAMASSA-HOLM TYPE EQUATIONS WITH DISSIPATIVE TERM

1IntroductionWe consider the Camassa-Holm type equations with dissipative termut?uxxt δuxxxx f(u)x=ε(2uxuxx uuxxx) g(x),x∈[0,1],t>0.(1.1)Under nonlinear boundary conditionu(0,t)=ux(1,t)=uxx(0,t)=0,t>0,(1.2)δuxxx(1,t)?εu(1,t)uxx(1,t)=?(u(1,t)),t>0,(1.     

SINGULAR SOLUTIONS FOR A CONVECTION DIFFUSION EQUATION WITH ABSORPTION

ＳＩＮＧＵＬＡＲＳＯＬＵＴＩＯＮＳＦＯＲＡＣＯＮＶＥＣＴＩＯＮＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮＷＩＴＨＡＢＳＯＲＰＴＩＯＮＺｈａｏＪｕｎｎｉｎｇ（赵俊宁）（Ｄｅｐｔ．ｏｆＭａｔｈ．,ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈａｎｇｃｈｕｎ１３００２３,Ｃ...     

一类带粘性项的抛物方程解的存在性和爆破性

该文研究具有多项式非线性项和粘性项的非线性抛物方程的初边值问题.在一定条件下,我们得到方程的弱解全局存在.在另一些条件下,我们得到该方程的解将在有限时刻爆破,并给出了爆破时间的上界,该上界受初始函数及其支集控制.该结论推广了Messaoudi在文献[15,16]中的工作.     

具有阻尼项的非线性波动方程的初值问题

本文研究具有阻尼项的非线性波动方程的初值问题ｕｔｔ－２ｂｕｘｘｔ＋ａｕｘｘｘｘ＝β（ｕｘ＾ｎ）ｘ,;ｕ（ｘ,０）＝ψ（ｘ）,ｕｔ（ｘ,０）＝ψ（ｘ）,其中ｂ〉０,β≠０为任意实数,ｎ≥２为整 当ａ≠ｂ＾２,ψ∈Ｌ１（Ｒ）∩Ｈ＾２（Ｒ）,ψ∈Ｋ１（Ｒ）∩Ｌ３（Ｒ）时,上述问题存在唯一的整体光滑解。     

EXISTENCE AND DECAY OF WEAK SOLUTIONS TO DEGENERATE DAVEY-STEWARTSON EQUATIONS

In this paper, the authors consider a system of degenerate Davey-Stewartson equations. They prove the global existence of weak solutions in some weighted function spaces and the decay of weak solutions in some anisotropic spaces for appropriate initial data.     

R^N中的非线性退化椭圆方程粘性解的存在性

本文研究了Ｒ＾Ｎ中的非线性退化椭圆型方程Ｆ（Ｄｕ，Ｄ＾２ｕ）＋ｕｓ＝ｆ的非负粘性解的存在性，其中ｓ〉０，Ｆ满足某些关于ｐ的条件，本文在下面的条件下证明了存在性；１．ｓ〉ｐ－１，ｆ在无穷远处不需要增长条件；２．０〈ｓ≤ｐ－１，ｆ在无穷远处具有某种增长条件。     

OSCILLATION OF A NONLINEAR DELAY DIFFERENTIAL EQUATION WITH NONLINEAR NEUTRAL TERM

This paper is concerned with the following nonlinear delay differential equation with nonlinear neutral term[h(t)(y(t) +φ(t,y(τ(t)))']' + q(t)f(y(g(t))) = 0. An oscillation criterion for the above equation is obtained.     

非线性四阶两点边值问题的一个正解存在定理

本文利用锥压缩锥拉伸型的Krasnosel’skii不动点定理证明了非线性四阶两点边值问题的一个正解存在定理．     

CAUCHY PROBLEM FOR A DEGENERATE PARABOLIC EQUATION WITH NON-DIVERGENCE FORM

In this article, it is shown that there exists a unique viscosity solution of the Cauchy problem for a degenerate parabolic equation with non-divergence form.     

GLOBAL BLOW-UP FOR A LOCALIZED DEGENERATE AND SINGULAR PARABOLIC EQUATION WITH WEIGHTED NONLOCAL BOUNDARY CONDITIONS

This paper deals with the blow-up properties of positive solutions to a localized degenerate and singular parabolic equation with weighted nonlocal boundary condi- tions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, the global blow-up behavior and the uniform blow-up profile of blow-up solutions are also described. We find that the blow-up set is the whole domain {0, a}, including the boundaries, and this differs from parabolic equations with local sources case or with homogeneous Dirichlet boundary conditions case.