查询词典 bounded domain

There are series of papers studying the solvability of an incompressible, viscous, instationary fluid contained in a domian bounded entirely by a free surface. In 1977, Solonnikov proved its local solvability in a Holder space for any initial date but without surface tension. In 1984, he considered the same problem in a Sobolev space with surface tension being taken into account. In I992, Mogilevskii and Solonnikov treated the same problem in a Holder space, where the coefficient of surface tension is not a constant. There are also short-time existence results for the solvability of an incompressible, vicous, unsteady fluid bounded above by a free surface and below by a fixed bottom which approach horizontal planes at infinity. In 1981, Beale proved its local solvability in a Sobolev space for any initial date but without surface tension. In 1983, Allain were concerned with the same problem in R〓 with surface tension but under the assumption that the initial fluid domain was near a horizontal strip. In 1987, he obtained the same result without the preceding assumption. In 1996, Tani solved the same problem in R with surface tension. For the solvability of an incompressible viscous instationary fluid in Ω R bounded inside by a free surface S and outside by a rotating boundary S, in 1995 Ciuperca proved its local existence in a Sobolev space for any initial date but without surface tension. In this paper, we consider the same problem with surface tension.

对于边界完全是由自由边界组成的有界区域中粘性不可压流体的非定常运动问题，Solonnikcv于1977年在忽略表面张力情况下证明了初值问题小时间解在Holder空间的存在性，于1984年在有表面张力情况下证明了初值问题问题小时间解在Sobolev空间的存在性，Mogilevskii和Solonnikov于1992年在表面张力系数可以不是常数情况下证明了初值问题小时间解在Holder空间的存在性；对于上面是自由边界、下面是固定边界且两边界在无限处趋于水平的无限区域中粘性不可压流体的非定常运动问题，Beale于1981年在忽略表面张力情况下证明了初值问题小时间解在Sobolev空间的存在性，Allain于1983年在有表面张力情况下证明了R中初值问题小时间解在Sobolev空间的存在性，但其中假定初始区域近似是个水平条，他于1987年去掉了这个假定得到同样的结果，Tani于1996年在有表面张力情况下证明了R中初值问题小时间解在Sobolev空间的存在性；对于R中内面是自由边界、外面是旋转边界S的有界区域中粘性不可压流体的非定常运动问题，Ciuperca于1995年在忽略表面张力情况下证明了初值问题小时间解在Sobolev空间的存在性，本文考虑了在有表面张力情况下初值问题可解性问题。

At last, it is proved for the two systems that when the control domain U is a bounded, closed set, the reachable set is the same as that when the control domain is the convex of U.It is an advancement for original results.

最后证明了当控制区域U是有界闭集时上述两个系统的等时区域与控制区域是U的凸包时的等时区域相同，推广了有限维的结论。

Transitivity determines whether the trust is bounded by the domain and the realm in the trust relationship.

传递决定信任是否被信任关系里的域和领域绑定。

Let f be defined for all nonnegative x, and suppose that it is continuous, strictly increasing and bounded on its domain.

令f定义在一切非负的x 上，并在定义域内连续、严格递增和有界。

In[5],combining the algebraic topology method,we have proven that conjunction matrix is complete topological invariant of bounded closed domain in plane under F-homeomorphism.so,for any two bounded closed domain in plane ?

主要原因在于拓扑不变量通常比较难算，没有比较实用的方法来恰当地提取图形的拓扑不变量，尤其是对较复杂的图形而言更是困难重重。

In this paper,we study the oscillation properties of solutions to the following problems of three classes of delay parabolic equations of neutral type.where Ω is a bounded domain in R~n with a piecewise smooth boundary ?

本文研究了三类中立型时滞抛物方程：解的振动性。其中G=Ω×(0，+∞)，Γ=Ω×0，+∞，ΩR~n是有界域，边界Ω逐片光滑，Δ是拉普拉斯算子，？

Model:The mathematic model of one kind of oin reactions for the problomof groundwater[47,48]:whereis a bounded domain with smoothy boundary.J=0,T.D＞d＞0is the diffusion coeffcients,ρ＞0 is the density of the solid,which are all constants.

模型：地下水污染问题中一类离子反应数学模型[47，48]：〓其中〓为具有光滑边界的有界区域，J＝0，T。这里D＞d＞0为扩散系数，ρ＞0为固体颗粒密度，均为常数。〓初边值条件为

The main goal of the thesis is to study such some problems as theexistence of weak solutions of quasilinear elliptic equations involvingcritical Sobolev exponents on a bounded domain and〓,the unique-ness of weak solutions、regularity of weak solutions、stability ofweak solution on exponent p、continuity of very weak solutions ondomains、the fusion problem of weak solutions and the existenceof minimal positive solution of a class of quasilinear elliptic obstacleproblems,which have been extensively concerned,but have not beensolved satisfactorily in the latest several years.

本文主要对近年来人们普遍关注而又没有完全解决的几个问题——有界域及无界域上带临界增长的拟线性椭圆方程弱解的存在性，弱解、很弱解的唯一性、正则性，解关于区域的连续依赖性，解关于指数的稳定性，弱解、很弱解的合并问题，以及椭圆型偏微分方程对应的障碍问题极小正解的存在性等进行研究。

Optimalerror estimates in L2-norm and H1-norm are obtained.Model:The mathematical model for two phase incompressible flow innaturally fractured reserviors is[34]:Supposeis a bounded domain with smoothy boundary,the rock ispresented byΩi,the volume of the fissures is small,Ωm=Ω.In the fissures Ω:s(x,0)=s0,x∈Ωin the rock Ωi:where J=0,T.

模型：裂缝孔隙介质中油水两相不可压缩驱动问题的数学模型为[34]：设〓为具有光滑边界的有界凸域，其中多孔岩块以Ωi表示，Ωm＝∑Ωi，因裂缝体积很小，可以认为Ωm＝Ω。x在裂缝系统Ω上：〓s(x，0)＝s0，x∈Ω在任一岩块Ωi上：〓其中J＝0，T。

Key words:Spectral and pseudospectral approximation,incompressible fluid flow,un-bounded domain,nonlinear partial differential equations.

本文的主要方法与技巧对无界区域中的其它偏微分方程同样适用。关键词：方法谱与拟谱逼近，无界区域，不可压缩流，非线形偏微分方程。收敛性和稳定性

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。