Asymptotic Behavior of the Finite Difference and the Finite Element Methods for Parabolic Equations

0IntroductionLeft(xΩ),b eg(a x)boaunnddeud0(d xo)maairne ibnouRndne,d a anndd a csosnutimneuo tuhsa t.We consider the followinginitial-boundary value problem u t(x,t)-Δu(x,t)=f(x),inΩ×R u|Ω=g(x),t>0u|t=0=u0(x),x∈Ω(1)whereΔis Laplace’s operator.Th     

带梯度项的发展P-Laplace方程解的耗竭

考察带梯度项的发展p-Laplace方程的第一初边值问题　ut - div(｜u｜p- 2u) = - λ｜u｜α- 1u ｜u｜β, x ∈Ω,t> 0,u = 0, x ∈Ω,t> 0,u(x,0) = u0(x), x ∈Ω,其中p > 2,λ,α和β为正常数,u0(x) ∈L∞(Ω) ∩W1,p0 (Ω).　　众所周知,若方程不带梯度项,上述问题的解当且仅当0 < α< 1 时在有限时间内耗竭.本文的目的是研究方程右边正的梯度项是否会影响解的耗竭性.应用能量方法,我们给出了解在有限时间内耗竭的充分条件.     

一类奇异半线性反应扩散方程组Cauchy问题解的Blow-up问题

研究了如下奇异半线性反应扩散方程组Cauchy问题:ut-(1/t)Δu=vp t>ε>0,x∈Rnvt-(1/t)Δv=up t>ε>0,x∈Rn(1)limt→εu(t,x)=u0(x)x∈Rnlimt→εv(t,x)=v0(x)x∈Rn(2)其中,p>1,u0(x),v0(x)∈L∞(Rn),u0(x)≥0,v0(x)≥0,且u0(x),v0(x)不恒为零.证明了其非负局部解在有限时间内Blow-up.     

包含临界指数的半线性椭圆型方程的正解

利用Sobolev-Hardy不等式和山路几何研究了如下包含临界指数的半线性椭圆型方程正解的存在性-div(|x|β(△)u)＝|x|αup-1+λ|x|σuq-1,x∈Ω;u＞0,x∈Ω;u=0,x∈(а)Ω.     

含p-Laplace算子的非线性方程的多解的存在性

利用变分方法证明了Neumann边值问题-△粯pu+α(x)up-2u=μf(x,u),x∈Ω5u5γ=0,x∈5在一定条件下一列弱解的存在性,其中△粯pu=div(1+èup2-2èu),p≥2,μ>0为实参数,α(x)∈L∞(Ω)且α(x)>0,f:Ω×R→R为满足一定条件的Carathoédory函数。     

一类半线性抛物型方程解性质的注记

在[1]中,研究了发生在燃烧问题和某些非线性扩散问题中的初边值问题:u_t-▽·(D(x)·▽u)=λ(e~(au)-b)(t>0,x∈Ω,)(1)β(()u)/(()v)) u=0(t>0,x∈()Ω)(2)u(0,x)=u_0(x)(x∈Ω),(3)其中Ω是在 R~n 内的一有界区域,()Ω是Ω的边界,λ、β、a、b 是非负常数,0≤6≤1,D 是在()(Ω的闭包)上的正函数,▽是在Ω内的梯度算子,()/(()v)是在()Ω上的外法向导数。     

一类反应扩散系统的全局存在性和爆破性

主要讨论如下反应扩散系统ut-Δu =um1vn1wl1,(x ,t) ∈Ω× (0 ,∞ )vt-Δv =um2 vn2 wl2 ,(x ,t) ∈Ω× (0 ,∞ )wt-Δw =um3 vn3 wl3 ,(x ,t)∈Ω× (0 ,∞ )u(x ,t) =v(x ,t) =w(x ,t) =0 ,(x ,t)∈ Ω× (0 ,∞ )u(x ,0 ) =u0 (x) ,v(x ,0 ) =v0 (x) ,w(x ,0 ) =w0 (x) ,x∈Ω　　其中ΩRn 中具有光滑边界的有界区域 , Ω ,m1 ,n2 ,l3≥ 0 ,n1 +l1 ,m2 +l2 ,m3+n3>0 (这些条件保证系统是完全耦合 ,u0 (x) ,v0 (x) ,w0 (x)是非负的 ,连续的有界函数 .这个系统来源于一个描述有 3种可燃混合物的热传导模型 .在这种情况下u ,v和w分别代表 3种混合物的温度 ,假定 3种物质的热传导性是相同的 .主要在Rn 中讨论了如下系统的爆破解的存在性ut-Δu =up1 vq1 ,vt-Δv=up2 vq2得到了解的爆破率     

一类非线性椭圆型问题爆炸解的存在性与全局最优估计

设f满足:H(t)=∫t∞f(dss)<∞,t∈R,∫-∞∞f(dss)=∞(或H(t)=∫t∞f(dss)<∞,t>0,∫0∞f(dss)=∞,且f'(t)∫t∞f(dss)在R(或(0,∞))上有界,构造爆炸上解和爆炸下解,得到了非线性椭圆型问题Δu=f(u),x∈Ω,u|Ω= ∞解的存在性和渐近行为的全局最优估计.     

一类具弱阻尼的奇性扰动Boussinesq型方程的位势井方法

采用位势井方法研究一类具弱阻尼的奇性扰动Boussinesq型方程的初边值问题utt-uxx-αux4-βux6 but=σ(u)xx,x∈Ω,t>0,u(0,t)=u(1,t)=uxx(0,t)=uxx(1,t)=ux4(0,t)=ux4(1,t)=0,t>0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,其中uxi=ixui,σ(s)是一个已知的非线性函数,α和β是两个正的实常数,b≥0是任意实数,Ω=(0,1).得到了相应初边值问题整体广义解的存在唯一性.     

一类四阶Navier边界值问题的高能量解

利用喷泉定理得到了一类四阶Navier边界值问题Δ2 u+cΔu=f(x,u)x∈Ωu=Δu=0 x∈{Ω无穷多个高能量解的存在性,其中ΩRN(N>4)是一个有界光滑区域.     

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     

An affordable accurate evaluation of the binding conformations predicted by molecular docking studies in bio-system

Franck-Condon factors bridge the gap between theoretical modeling and experimental observations for molecular electronic spectroscopy and electron transfer.Under the displaced harmonic oscillator approximation,multidimensional Franck-Condon factors are decomposed into a product of many one-dimensional(1D)Franck-Condon(FC)factors,and each 1D-FC factor is associated with one Huang-Rhys factor that determines the leading contribution of     

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