查询词典 exterior boundary problem

In this dissertation, the author discusses the numerical solution for the direct acoustic scattering problem with the Neumann boundary condition, and pays more attentions to discuss numerical recovering the shape of the obstacle region, which is the inverse problem of the direct acoustic scattering problem with the Dirichlet or impedance boundary condition.

本文重点研究了Neumann边界条价下的声波障碍散射正问题和Dirichlet、Impedance边界条件下的声波障碍散射区域反问题的数值计算方法，得到很好的理论结果和数值结果。

In this paper,regularization method is introduced. The author pays more attentions to investigate the numerical solution for the direct acoustic scattering problem with the Dirichlet boundary condition, and the numerical recovering the shape of the obstacle region which is the inverse problem of the direct acoustic scattering problem with the Dirichlet boundary condition.

本文主要引入正则化方法，研究了针对Dirichlet边界条件的声波障碍正散射问题和声波障碍散射反问题的数值计算方法，并得到了很好的数值结果。

For the first time, in [3] the authors discussed the inequalities of B-B and by using them the authors give a proof of the existence and uniqueness of the generalized solution for magnetostatic field problem with zero boundary value. By using the inequalities of B--H in, in[-5,6] the authors give a proof of the existence and uniqueness of the generalized solutions for 3-D magnetostatic field Neumann problem and 2-D magnetic field first boundary value initial problem.

前人已讨论了B—H间的几个基本不式，并由之证明了三维静磁场带零边值问题广义解的存在与唯一性，作者也曾利用给出的B—H间的不式证明了三维静磁场Neumann问题和二维时变场第一边值初值问题广义解的存在与唯一性。

In this paper,we consider the existence and uniquness of solution for Dirichlet problem of the Helmholtz equation on the domain with corners, i.e problemFor smooth boundary,we use potential theory to transform the problem into second kind boundary integral equation ,and use Fredholm alternative theorem,we obtain the existence and uniqueness of Dirichlet problem.

在本文中，我们考虑边界含尖点的有界区域上Helmholtz方程△u+k~2u=0的Dirichlet问题即问题与问题解的存在及唯一性。

There is no difficulty for us to solve N-K problem for submerged bodies by the coupled element method, but for wavemaking problems of the bodies piercing free surface, we get a difficult problem of line integral on the free surface when we solve the boundary value problem in the external region by boundary element method.

对于深潜物体的N—K问题，用耦合元方法求解不存在根本性的困难，但对于水面船波兴波问题，采用边界元方法来处理外域中的边值问题而出现了所谓的自由面线积分问题。

Based on the fundamental principles of the improved method mentioned above, multi-functional computation software package, which can be used to analyze effectively the interference effects of random flaws in plane problem, boundary problem and space problem, is compiled and a number of problems involved in the interference effects of different kinds of flaws such as random equal length through-cracks, random branched throughcracks, random unequal length through-cracks, random holes to through-cracks, unequal length edge cracks, equal length and distance multiple edge cracks, random notches with different aspect ratio, random notch to edge crack, non-coplanar surface cracks with different aspect ratio, staggered surface cracks, surface crack to embedded crack and embedded cracks near free boundary are analyzed and computed by the package.

依据上述改进法的基本原理，本文编制了能有效地分析平面问题，边界问题及空间问题的任意缺陷群相互干涉效应的多功能计算软件包。据此，本文分析计算了各类缺陷群。诸如，任意等长裂纹群。任意折裂纹群；任意不等长裂纹群，任意孔与裂纹群，不等长边裂纹群。等长等间距多裂纹群，任意形状比缺口群，任意缺口与边裂纹，非共面不同形状比表面裂纹群，交错型表面裂纹群，表面裂纹与埋藏裂纹群及自由边界附近埋藏裂纹群等的相互干涉效应问题。

In this paper,the Riemann boundary value problem for bianalytic vector function s is investigated using the theory of boundary value problem for analytic functions,we have not only found the solution method for bianalytic vector function s,but also established an explicit form of the general solution and the conditions for the solvability of the above problem.

利用解析向量函数边值问题理论，提出了双解析向量函数的R iem ann边值问题，并研究了问题的解法和解的一般表达式及可解性条件，得到了相应的可解性定理，同样方法可解决多解析向量函数的边值问题

The gap element method is proposed in the paper for two kinds of problems, which include contact problem and gap joint problem. Elasticity contact problem falls into the category of unknown boundary value problems. It follows that the contact area and contact conditions or states can never be determined without special mathematical analysis, which is a very difficult work. The boundary conditions of the contact surfaces are deduced.

文中给出了间隙元法在空间可动部件接触问题中的应用，推导了其几何边界条件和力学边界条件，利用虚功原理推导了含间隙元弹性接触问题的有限元方程式，给出了其数值解法的迭代步骤，并指出了利用间隙单元进行分析的特点。

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。

Secondly, based on the different structure characteristics and additional conditions, we study several kinds of inverse problems of pseudoparabolic equations. One is a kind of pseudoparabolic inverse problem of identifying a constant coefficient solved by combining the formal solution of the problem and the additional condition properly. The second is the pseudoparabolic inverse problems of identifying an unknown boundary function and an unknown source term solved by using the Riemann function method to get the formal solution of the problem and then using the additional condition to transform the problem into a Volterra integral equation of the second kind. The third is a kind of backward heat flow problem of nonlinear pseudoparabolic equation solved by combining the Riemann function method and the fixed point theory properly.

其次，根据不同模型的结构特点和附加条件，研究了几类伪抛物型方程的反问题：一是利用问题的形式解并结合附加条件，解决了一类伪抛物型方程常数系数的反问题；二是利用Riemann函数方法获得问题的形式解，利用附加条件将问题转化成求解第二类Volterra积分方程问题，解决了一类伪抛物型方程未知边界值的反问题和未知源项的反问题；三是将Riemann函数方法和不动点定理相结合，解决了一类非线性伪抛物型方程的后向热流问题。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。