一类弱耗散双组份Hunter-Saxton系统的爆破与爆破率

研究了一类周期弱耗散双组份Hunnter-Saxton系统的爆破现象.首先,给出了此类Hunnter-Saxton系统解的局部适定性及其精确的爆破机制;其次,证明了在一定的初始值下Hunnter-Saxton系统强解的几个爆破结果;最后,给出了HunnterSaxton系统强解的爆破率.     

具零阶耗散的双成分Camassa-Holm方程的整体解和爆破现象

本文研究了具零阶耗散的双成分Camassa-Holm方程的Cauchy问题.由Kato定理得到局部适定性的结果,然后研究了解的整体存在性和爆破现象.     

Hyperelastic Rots方程在Besov空间的局部适定性

借助Littlewood-Paley分解,研究了hyperelastic rots方程在Besov空间的Cauchy问题,建立了该方程在 Besov空间的局部适定性定理,进一步还讨论了该方程解的爆破准则.     

带加性白噪声的随机广义Boussinesq方程解的爆破性

本文研究一维空间中带加性白噪声的随机广义Boussinesq方程.首先运用截断方法,建立该方程Canchy问题解的局部适定性,然后运用It(o)公式导出了该系统的能量方程,最后证明了该系统解的爆破性.     

具有较高级算子的两组分Camassa-Holm方程的柯西问题

讨论了具有高阶算子-(1-_x~2+_x~4)的两组分Camassa-Holm方程在Sobolev空间H~s,s>5/2中的柯西问题,利用构造逼近解方法证明了该方程解的局部适定性问题,同时应用能量估计及嵌入定理等方法得到了在给定初值条件下的爆破准则,并且进一步给出了具体的爆破速率.     

一类弱耗散Camassa-Holm 方程Cauchy问题在Besov 空间解的局部适定性

利用Littlewood-Paley 理论和输运方程解的先验估计, 在Besov 空间 中证明了一类弱耗散Camassa-Holm 方程Cauchy 问题解的局部适定性, 同时给出了解的能量估计及爆破准则.     

弱耗散非线性浅水波方程周期柯西问题

建立了弱耗散非线性浅水波方程的局部适定性,对于不同的初始值,我们分别得到了解的整体存在性和解的爆破。     

带真空无磁扩散不可压磁流体方程柯西问题的局部适定性

该文讨论了在真空远场的密度条件下,二维不可压零磁耗散磁流体力学方程组柯西问题的局部适定性.在初始密度和磁场具有一定的衰减性时,证明了磁流体方程具有唯一的局部强解.当初值满足兼容性条件和适当的正则性条件时,该强解就是经典解.除此之外,文中还给出了一个仅与磁场有关的爆破准则.     

半线性Schrdinger方程初值问题的H~1-适定性

在RN(N≥2)中讨论一类具时间依赖系数的半线性Schrdinger方程初值问题的H1-适定性.通过Strichartz估计和解的先验估计,得到了系数零点阶数λ与临界适定指数σ之间的关系,在一定条件下证明了该问题的H1-局部适定性和整体适定性.     

带密度的不可压Euler方程在临界Besov空间中的适定性

本文证明了带密度的不可压Euler方程在临界Besov空间中的局部适定性,并且只用涡度场给出了强解的一个爆破准则.另外,本文关于带密度的不可压磁流体方程得到了类似结果.     

一类非线性抛物方程组解的爆破时间上下界估计

本文研究了一类非线性抛物方程组uj/t=△uj+fj(u)解的爆破时间的估计问题.通过构造恰当的辅助函数和建立一系列微分不等式,获得了此类非线性抛物方程组解的爆破时间上下界的估计.从而将单个方程的结论推广到了方程组的情形.     

THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

1IntroductionThispaperisconcernedwithpositivesolutionOfthesemilinearheatequationswithlocalizedreactionssubjecttoeitherinitialconditions(Cauchyproblem)ortheinitialandboundary-value(DirichletorNeumanntype)conditionswherenisaboundeddomaininRe,icEO.Equations(1.1)canbethoughtofasamodeltodescribesomephysicalphenomena(heatpropagation,chemicalreaction)inwhichthenonlinearreactionsinadynndcalsystemtakesplaceonlyatasinglesite.InthesequelforconvenienceweshallsamplycalltheCauchy,initial-Direchlet,orini…     

THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

1IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblem,where"o(x)isnon-negativesmoothfunctionsatisfying"o.(0)=0,"o.(1)=1'Whenconsideringtheblow-upofsolution,thefollowingproblemarisenaturally:Doesblow-upoccur?Howdoesthesolutionapproachtheblow-uptime'!Andwilersisthehotspotlocated(blow-upset)?WelookattheheatequationwithanonlillearboundaryconditiollHerefiisaboundeddomaininR",p>1isarealnumber.IthasbeenknownforalongtimethattheDroblelil(1.1).(1.2)withAL(~,0)--'no(x)doesnothaveaglobals…     

THE SIMULTANEOUS AND NON-SIMULTANEOUS BLOW-UP CRITERIA FOR A DIFFUSION SYSTEM

This paper investigates the finite time blow-up of nonnegative solutions for a nonlinear diffusion system with a more complicated source term,which is a product of localized source,local source,and weight function,and complemented by homogeneous Dirichlet boundary conditions.The criteria are proposed to identify simultaneous and nonsimultaneous blow-up solutions.Moreover,the related classification for the four parameters in the model is optimal and complete.The results extend those in Zhang and Yang [12].     

具有非线性边界条件半线性热方程组解的爆破性质

本文考虑一类半线性热方程组的解,给出了解爆破的充分必要条件,爆破速率和爆破点的位置。     

两类Chemotaxis模型解的性质

本文讨论了抛物-双曲和抛物-常微两个Chemotaxis模型初边值问题解的性质.利用形式级数展开的方法，得到全局解在微小扰动下，导致解在有限时间内爆破，并对爆破时间进行了估计.因此说明了这种模型空间齐性解的不稳定性。     

BLOW-UP OF THE SOLUTION FOR A KIND OF HIGHER ORDER HYPERBOLIC EVOLUTION SYSTEMS

In this paper, we give some results on the blow-up behaviors of the solution to the mixed problem for some higher nonlinear hyperbolic evolution equation in finite time. By introducing the "blow-up factor K(u,ut)" we get some new results, which generalize the conclusions of [3] and [4].     

Non-simultaneous blow-up in localized reaction–diffusion equations

This article deals with blow-up solutions in reaction–diffusion equations coupled via localized exponential sources, subject to null Dirichlet conditions. The optimal and complete classification is obtained for simultaneous and non-simultaneous blow-up solutions. Moreover, blow-up rates and blow-up sets are also discussed. It is interesting that, in some exponent regions, blow-up phenomena depend sensitively on the choosing of initial data, and the localized nonlinearities play important roles in the blow-up properties of solutions.     

REMARK ON THE BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE NAVIER-STOKES EQUATIONS IN MULTIPLIER SPACES

In this note, we prove that Xr （0 〈 r 〈 1） norm of the vorticity controls the blow-up phenomena of strong solutions to the Navier-Stokes equations in R3.     

Total versus single point blow-up in a localized heat system

This paper considers a heat system with localized sources and local couplings subject to null Dirichlet boundary conditions, for which both total and single point blow-up are possible. The aim of the paper is to identify the total and single point blow-up via a complete classification for all the nonlinear parameters in the model. As preliminaries of the paper, simultaneous versus non-simultaneous blow-up of solutions is involved, too. The results are then compared with those for another kind of heat system coupled via localized sources in a previous paper of the authors.