一类拟线性退化椭圆方程Dirichlet问题粘性解的C^α正则性

讨论了一类拟线性退化椭圆方程Dirichlet问题{-Tr[α（x）D^2u] H(x,u,Du)=0,x∈Ωu=φ,x∈aΩ粘性解的C^n正则性,证明了当方程及边界满足一定条件时,若边值φ（x）∈C^α（aΩ）,则粘性解u(x)∈C^α（Ω^-)。     

一类奇异非线性Dirichlet问题解的存在性

主要采用上下解方法,并结合极大值原理证明了一类奇异非线性Dirichlet问题-Δu=b(x)g(u)+λa(x)f(u),u0,x∈Ω,u|Ω=0解的存在性.其中Ω为Rn(n≥2)中的有界光滑区域,λ0,g在0处有奇性,且g'(s)0,s∈(0,∞),f∈C([0,∞),[0,∞))∩C1((0,∞)),b,a0在Ω上局部Hlder连续.     

β+1

张亚阳  汤军健 《渤海大学学报(自然科学版)》2006,(4)

一类非线性波动方程的柯西问题

文章主要考察一类非线性波动方程uu+uxxxx+λu=σ(ux)x,λ>0的柯西问题解的存在性和唯一性.当σ(ux)x=-β(|ux|pux)x,β>0,p>0时,通过构造稳定集(位势井)W={u∈H2(R)|‖uxx‖2+λ‖u‖2<2(p+2)/pd}和不稳定集V={u∈H2(R)|‖uxx‖2+λ‖u‖2>2(p+2)/d},得到了W和V在上述方程的流下是不变的,并证明了如果初始能量E(0)≤d,那么当初值u0∈(-W)时,问题存在惟一整体解u∈C1([0,∞);H2);当初值u0∈V时,问题的解在有限时刻T1∈(t1,t1+4φ(t1)/pφ'(t1))发生爆破.     

临界半线性双调和方程非平凡解的存在性

在有界光滑区域Ω?RN上研究临界半线性双调和方程Δ2u＝λu＋|u|q－2u,λ>0,u∈H0(1) (Ω)∩H2(Ω)非平凡解的存在性.利用极小极大原理和山路引理,证明方程所对应的泛函存在临界点,从而得到方程至少存在一个非平凡解的结论.     

一类拟线性退化椭圆方程Dirichlet问题粘性解的C~α正则性

讨论了一类拟线性退化椭圆方程 Dirichlet问题　 - Tr[a(x) D2 u] H (x,u,Du) =0 ,x∈Ω　　　　　　　　　　　　　 u =ψ,x∈ Ω粘性解的 Cα 正则性 ,证明了当方程及边界满足一定条件时 ,若边值ψ(x)∈ Cα( Ω ) ,则粘性解 u(x)∈ Cα(Ω ) .     

带阻尼项的非自治2D Navier-Stokes方程的一致吸引子

考虑带阻尼项c uβu的非自治2DNavier-Stokes方程解的长时间动力学行为,应用一些新结果和能量估计技巧,获得了能量的一致衰退估计.结果表明,当外力项满足正规条件(而非平移紧),阻尼项参数c0,1/3≤β≤2,初值uτ∈cl(H10(Ω))2{u∈C∞0(Ω)2,div u=0}时,阻尼型非自治2D Navier-Stokes方程满足一致(C)条件,从而证明了一致吸引子在cl(H10(Ω))2{u∈C∞0(Ω)2,div u=0}内的存在性.     

粘弹性流体的一个爆破准则与存在性结果

我们给出描述粘弹性流体的Oldroyd方程的一个爆破准则,即∫T*0‖(△)u‖L∞dt= ∞.在较弱的条件下,即当初值(φ)0∈W2,q(Ω),3＜q≤6, u0∈H10∩H2时,同样得到了强解的局部存在惟一性,从而改进了林芳华、柳春和张平的一个结果.     

一类双重退化渗流方程解的存在性

结合Fichera-Oleinik理论,研究一类双重退化渗流方程ut=div(ρα#um),(x,t)∈QT=Ω×(0,T)的可解性问题.其中Ω是RN中的有界区域,边界Ω充分光滑,ρ(x)=dist(x,Ω),m1,α≥2,u0非负,u0∈Lm+1(Ω),ρα/2#um0∈L∞(0,T;L2(Ω)).借助于一般粘性解的定义,给出了该渗流方程存在具有齐次边界条件的弱解的定义,并证明其存在性.     

β+1＜p＜α+2＜p+p(β+1)/n时解的全局存在性

证明了当max(β+1,p)＜α+2＜p+p(β+1)/n时,且当初值属于某一类稳定集时,问题d/(at)(|u|β-1u)-Div(|▽u|p-2▽u)=▽·B(u)+|u|au;x∈Ω,t∈(0,T]u(x,t)=0; x∈(a)Ω,t∈(0,T]u(x,0)=u0(x); x∈Ω的全局解存在.     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

Features of Women's language

Language is a means of verbal communication. People use language to communicate with each other. In the society, no two speakers are exactly alike in the way of speaking. Some differences are due to age, gender, statue and personality. Above all, gender is one of the obvious reasons. The writer of this paper tries to describe the features of women＇s language from these perspectives： pronunciation, intonation, diction, subjects, grammar and discourse. From the discussion of the features of women＇s language, more attention should be paid to language use in social context. What＇s more, the linguistic phenomena in a speaking community can be understood more thoroughly.     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

On the Thermodynamic Limit for Responses to Static Electromagnetic Fields

For molecular systems,the quantum-mechanical treatment of their responses to static electromagnetic fields usually employs a scalar-potential treatment of the electric field and a vector-potential treatment of the magnetic field.Although the potential for each field separately is associated with the choice of an(unphysical)origin,the precise choice of the origin for the electrostatic field has little consequences for the results.This is different for the     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with     

Journal of Donghua University ( English Edition) Contents of Volume 31

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