一类具局部化源的反应扩散方程解的整体爆破

研究带有齐次Dirichlet边界条件的反应扩散方程ux=△u+a(x)f(u)h(u(x0,t)),x∈Ω,t>0的解的爆破性质,在一定条件下,我们证明了解在有限时刻爆破,且爆破点集是整个Ω区域.     

非线性Sine-Gordon方程解的爆破和生命跨度

在Ω×[0,T)中考虑如下非线性Sine-Gordon方程初值问题解的爆破{utt-uxx=-sin u, x∈Ω;u(x,0)=u0(x), x∈Ω;ut(x,0)=u1(x), x∈Ω.这里,Ω是R中具有光滑边界(δ)Ω的有界域.在Dirichlet边界条件下,得到了其解爆破的若干充分条件,然后通过能量方法,得到了解的生命跨度的上界估计.     

一类四阶波动方程的弱解

研究下列初边值问题:utt αΔ2u-bΔut ututr g(u)＝0 in Ω×(0,∞);u(x,0)＝u0(x),ut(x,0)＝u1(x,0),x∈Ω;u＝(u)/(υ), x∈Ω的整体解的存在性和不存在性,以及整体解的惟一性和能量估计.这里Ω是Rn(n≥1)中的有界区域.借助于乘子方程,推出了整体解的能量衰减率.借助于势井理论,得到了在有限时刻内爆破的充分条件.由Galekin 近似方法得到解的存在性.     

一个带加权使局部源抛物型方程解的整体爆破

考虑带齐次Dirichlet边界条件,具使局部源项的抛物型方程ut=Δu＋a（x）epu＋qu（x0,t）,x∈Ω,t〉0的解的爆破性质,我们证明了当p〈0且p＋q〉0时,解在Ω内处处爆破.     

带非局部源和吸收项的p-Laplace方程解的性质

研究一类带齐次Dirichlet边界条件的P-Laplace方程ut-div(｜▽u｜p-2▽u)=∫aouqdx-kum,x∈Ω,t＞0解的爆破性质.其中P>2,q,m≥1,k＞0,Ω是RN (N≥1)上边界光滑的有界区城.在一定条件下,运用比较原理和上下解技巧,得到了正解的整体存在性与有限时刘爆破的结论.     

障碍最优控制问题的正则性

1IntroductionIn this paper,we consider the following opti malcontrol problem.Problem(C)Find a-y∈H01(Ω),such thatI(-y)=infy∈H01(Ω)I(y),(1)whereI(y)21∫Ω{|T(y)-z|2 |y|2}dx,y∈H01(Ω),(2)andΩ∈Rnis a bounded domain with a boundaryΩ∈C1,andz∈L∞(Ω)is a giventarget profile.In ad-dition,φT(y)is the solution of thefollowing varia-tional inequality(also called state equation):φ∈K(y)={v∈H01(Ω)|v≥y,a.e.x∈Ω},∫Ωφ(v-φ)dx≥0,v∈K(y).(3)As is known,for everyy∈H01(Ω),(3)adm…     

椭圆型方程解的连续性

考虑积分形式的椭圆型方程∫Gv,αα^αβ(x)u,β vf(x)]dx=0(A↓v∈W02^1(G))，在关于f(x)的较弱条件下，借助Green函数，证明了方程的弱解在区域内部的连续性。同时还考虑了下面的方程：∫Gv,αα^αβ(x)u,β vαg^α(x)]dx=0(A↓v∈Wo2^1(G))。     

带非局部源项的退化抛物方程的爆破

讨论了一类带有变指标反应项的非局部退化抛物方程ut=Δ(um)+∫Ωup(x)dx的爆破行为。运用特征函数方法和上下解方法,得到了该方程非负解的整体存在和有限时刻爆破的条件。     

一类临界指标椭圆方程解的存在性

运用变分方法及Hardy不等式讨论了下列椭圆方程: -Δu-μu/x2==u2*-1+u,x∈Ω其中该方程满足条件u>0,x∈Ω和u=0,x∈Ω,并且、μ<-μN-2/2,2*=2N/N-2.N≥3,Ω(∈ )RN是包含0的有界光滑区域;并且获得该方程解的存在性.     

具非线性边界条件的非线性抛物型方程解的Blow-up

利用能量方法讨论初边值问题 : u t = (a(u) u) +f(u) ,　　x∈Ω ,t >0 (1 ) u y =σ(u) ,　　　　　x∈ Ω ,t>0 (2 )u(x ,0 ) =u0 (x)　　　　　　x∈Ω ,(3 )的解的爆破性质 ,不限制f(u)与σ(u)正负 ,给出了此问题的解爆破的充分条件。部分证明了文 [4]的猜想     

一类具有位势的薛定谔方程的全局存在性和爆破门槛

通过使用变分和构建不变流形的方法,得到了一类具有位势的非线性薛定谔方程的解的全局存在性和爆破门槛．谋取,n-维欧氏空间的中一类非线薛定谔方程解的爆破和全局存在性．     

卡思卡特城堡

It is worthy of noting that, whilst Crookston Castle witnessed the earlier and happier portion of Mary's variegated life,     

Western and Eastern culture differences in commercial field

The communication of people partially is the communication of cultures. Culture has a direct effect on international commercial activities in all aspects. Different conceptions about time, space, equality, law and the like, lead people to deal with things in different ways. So to know cultures of the counterpart is to facil-itate our enterprises so as to have a smooth and successful communication in commercial activity.     

不同的吃喝玩乐

一、吃和喝吃苹果 eat an apple, 吃药 take medicine,吃糖 have some sweets,吃饭 have one's meals,吃馆子 dine out,吃惊 be surprised/     

漏洞百出的教育

Many college freshmen arrive woefully unprepared to do college work, and as disadvantaged populations continue to grow, the share of the American work force that has made it through college is expected to plummet. Many experts blame that educational failure not just on high schools but also on colleges. School & College, a special report by The Chronicle, looks at efforts to fix the system. What reforms would better prepare students for college? What should schools and colleges be doing differently? How should state and federal officials help?     

只要努力,不要后悔

There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love.     

浅谈移民问题

Migration occurs behind a variety of reasons and has a great effect on the whole world. People may migrate in order to improve their economic situation, or in order to escape civil strife, persecution, and environmental disasters. The impact of migration is complex, bringing both benefits anddisadvantages. This paper briefly talks about the causes of migration, the allocation of benefits, and the ways in which individual countries and the international community deal with this important subject.     

Sister Carrie, an Adherent of Desires

Sister Carrie is one of the most controversial characters in American literature.Thought as a "fallen woman" firstly,she was defined as a "new woman" by some critics later. However, by digging into the motivaton behind the whole process of Carrie's "success", the relationship between Carrie and her creator (the author), the social conditions of then American, it can be found that Carrie has never been free-standing on her thought and she has never found her real-sdf even after becoming a famous actress. In a society dominated by mass consumerism Carrie is only an adherent of her own desires. She also is a representative of all those country girls flooded into cities, a symbol and a sacrifice of the urbanization of America in a time countryside was overcome by cities.     

Improvement of one-cycle controller by use of proportional integral differential controller

1.IntroductionOne-cyclecontrolmethod,whichwasproposedaboutonedecadeago[1],hasbecomeanattractivemethodinspecialfieldssuchaspowerfactorcorrection[2-6],switchingamplifiers[7,8],etc.Themainideaofthiscontrollerisbasedonintegrationofdiodevoltageinone-cycleandforcesittobeexactlyequaltothereferencevalue.Themainadvantageofthiscontrollerisitsrealtimeabilitytorejectthevariationofinputvoltage[1].Despitethisgreatability,ithasnogoodperformancesinrejectingofloaddisturbanceandfollowingreferencecommands.Espec…