一个耦合系统自由边界问题的整体古典解

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｄｉｓｃｕｓｓｔｈｅｇｌｏｂａｌｃｌａｓｓｉｃａｌｓｏｌｕｔｉｏｎｏｆａｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｑｕａｓｉｓｔａｔｉｏｎａｒｙｐｒｏｂｌｅｍ .Ｔｈｅｐｒｏｂｌｅｍｃｏｍｅｓｆｒｏｍｔｈｅｄｉｓｃｕｓｓｉｏｎｏｆａｇｒｏｗｔｈｍｏｄｅｌｏｆｓｅｌｆｍａｉｎｔａｉｎｉｎｇｐｒｏｔｏｃｅｌｌ(ｓｅｅ [1— 3])ｉｎｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｃａｓｅ .Ｔｈｅｐｒｏｔｏｃｅｌｌｃａｎｂｅｖｉｓｕａｌｉｚｅｄａｓｈａｖｉｎｇａｐｏｒｏｕｓｓｔ…     

面积比较与上调和函数及其应用

本文研究了无穷远处具非负截曲率的完备非紧流形的几何和解析性质,并将 它应用于调和映照.     

积域上一类奇异积分算子的L~p有界性

本文证明,对于Ω∈(1)∩L(log~+L)~2(S~(n-1)×S~(m-1)),h(r,s)∈L~∞(R_+~1×R_+~1)和P_(N_1),P_(N_2)∈(2),带粗糙核的奇异积分算子为L~p有界。     

关于猝灭问题的一些结果及其应用

本文研究一类含奇异项的半线性抛物方程的初边值问题,给出了该问题的古典解整体存在或发生猝灭现象的判据以及猝灭解的生命跨度估计。同时,还用上述结果研究了一类含超Sobolev临界指标的半线性椭圆方程的Dirichlet边值问题,获得了正解的存在性结果。     

关于Morse引理的推广

Morse Lemma是奇点理论中一个极为重要的结论。[1]的作者称其文中的定理1和定理2是Morse Lemma的推广。为此我们愿就[1]中的几个问题与[1]的作者商榷。     

半线性热方程精确内部能控性

主要采用了构造辅助系统u′ △u=0的方法，同时也利用了强单调算子 的满射性。在条件（H)的修改下，得到在有限时间内的精确可控性，研究半线性热方程系统ey/et=△y-f(x,t,y,倒△y) h(x,t)的精确内部能控性。     

Arbitrarily large solutions of the conformal scalar curvature problem at an isolated singularity

We study the conformal scalar curvature problem

where is a continuous function. We show that a necessary and sufficient condition on for this problem to have positive solutions which are arbitrarily large at is that be less than 1 on a sequence of points in which tends to .

     

Well-posedness of the time-varying linear electro-magnetic initial-boundary value problem

The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday's law of electromagnetic induction and the initial-boundary conditions considered as constraints. Gauss's formula applied to a multi-medium region is used to derive the energy-estimating inequality. After converting the initial-boundary conditions into homogeneous ones and analysing the characteristics of an operator introduced according to the total current law, the existence, uniqueness and stability of the weak solution to the initial-boundary value problem of the time-varying linear electromagnetic field are proved.     

Long lasting phosphorescent properties of Ti doped ZrO2

A novel long-lasting afterglow phosphor ZrO₂:Ti is prepared by the conventional solid-stated method and their luminescent properties are investigated. A bluish white strong and broad emissive band, which is attributed to originate from the recombination of electrons trapped by F⁺ centers and the holes created in Valence band, is observed under 254 nm UV irradiation. The identical color long afterglow, which lasts about 1 h, is found in the ZrO₂:Ti phosphor after removing the 254 nm UV light. The mechanism of the long lasting phosphorescence (LLP) has been discussed based on the thermoluminescence (TL) results. The replacement of Zr by Ti produces more anion vacancies, resulting in the enhanced photoluminescence (PL) and LLP of ZrO₂:Ti sample. These results indicate that ZrO₂:Ti phosphor has potential promising applications.