共查询到20条相似文献,搜索用时 31 毫秒
1.
Dagmar Medková 《Czechoslovak Mathematical Journal》1998,48(4):763-784
For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series. 相似文献
2.
The jump relations of the quadruple layer potential on a regular surface in three dimensions are derived. The jumps are shown to be proportional to the product of the density of the potential and the mean curvature of the underlying surface. 相似文献
3.
The boundary value problem for the Laplace equation is studied on a domain with smooth compact boundary and with smooth internal cracks. The Neumann or the Robin condition is given on the boundary of the domain. The jump of the function and the jump of its normal derivative is prescribed on the cracks. The solution is looked for in the form of the sum of a single layer potential and a double layer potential. The solvability of the corresponding integral equation is determined and the explicit solution of this equation is given in the form of the Neumann series. Estimates for the absolute value of the solution of the boundary value problem and for the absolute value of the gradient of the solution are presented. 相似文献
4.
This note investigates the simple layer potential method for domains having external corners. The singular behaviour of simple layer density at the corners is studied for the Neumann problem of Helmholtz's equation. A numerical technique of solving the integral equation for this problem is proposed. This technique takes the singularity of the solution into consideration. Some numerical examples are given to show the applicability of the present method. 相似文献
5.
Dagmar Medková 《Applications of Mathematics》1998,43(2):133-155
For open sets with a piecewise smooth boundary it is shown that we can express a solution of the Robin problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. 相似文献
6.
Johannes Elschner 《Applicable analysis》2013,92(1-4):117-134
We consider the integral equation, (λ-K)u=f, where K is the double layer (harmonic) potential operator on the boundary of a bounded polyhedron in R3 and λ∣λ∣≥1 is a complex constant. We study the mapping properties of λ - K in weighted Sobolev spaces, applying Mellin transformation techniques directly to the integral equation. 相似文献
7.
O. Steinbach 《Journal of Mathematical Analysis and Applications》2004,294(1):1-6
We prove that the single layer potential operator of planar linear elastostatics is elliptic in [H−1/2(Γ)]2, if the domain Ω is scaled appropriately. 相似文献
8.
We consider a symmetric Galerkin boundary element method for the Stokes problem with general boundary conditions including slip conditions. The boundary value problem is reformulated as Steklov–Poincaré boundary integral equation which is then solved by a standard approximation scheme. An essential tool in our approach is the invertibility of the single layer potential which requires the definition of appropriate factor spaces due to the topology of the domain. Here we describe a modified boundary element approach to solve Dirichlet boundary value problems in multiple connected domains. A suitable extension of the standard single layer potential leads to an operator which is elliptic on the original function space. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
9.
10.
In this paper, the existence of boundary layer solutions to the Boltzmann equation for hard potential with mixed boundary condition, i.e., a linear combination of Dirichlet boundary condition and diffuse reflection boundary condition at the wall, is considered. The boundary condition is imposed on the incoming particles, and the solution is supposed to approach to a global Maxwellian in the far field. As for the problem with Dirichlet boundary condition (Chen et al., 2004 [5]), the existence of a solution highly depends on the Mach number of the far field Maxwellian. Furthermore, an implicit solvability condition on the boundary data which shows the codimension of the boundary data is related to the number of the positive characteristic speeds is also given. 相似文献
11.
微通道液体流动双电层阻力效应 总被引:3,自引:0,他引:3
采用数值方法求解双电层的Poisson-Boltzmann方程和液体运动的Navier-Stokes方程,研究微通道双电层对压强梯度液体流动的阻力效应. 量纲分析表明,双电层阻力大小可以用一个无量纲的电阻力数表示.它与液体的介电系数、固体表面的zeta电位平方成正比,与液体的动力粘性系数、电导率以及微通道的宽度平方成反比.在计算流动诱导的流动电位势和电阻力时,提出电流密度平衡条件,可以消除传统电流平衡条件导致的固壁附近产生局部回流的不合理物理现象.还给出不同电阻力数的微通道流量、流量损失率、速度剖面的数值结果,合理解释了双电层对微通道液体流动的阻力效应. 相似文献
12.
S. F. Shishkanova 《Journal of Mathematical Sciences》1993,65(4):1801-1803
Using a bulk potential, we construct a one-dimensional toroidal layer with corresponding density for the mass distribution. We determine the density of a simple layer, and also find the potential of a simple layer distributed along the surface of an elliptical torus of revolution with density depending on distance as measured along the normal between a tangent plane and the center of the torus.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 29, pp. 85–87, 1989. 相似文献
13.
Tongkeun Chang 《Potential Analysis》2008,29(2):105-117
In this paper, we show the existence of the solutions of the screen problems of the Stokes equation in R
n
, n ≥ 3. For the purpose of it, we use the fractional layer potentials (for the Stokes equation) in a bounded Lipschitz domain
The author is supported by the Korea Research Grant Foundation Grant (MOEHRD)KRF-2005-214-C00179. 相似文献
14.
Xiongfeng Yang 《Journal of Mathematical Analysis and Applications》2008,345(2):941-953
The study on the boundary layer is important in both mathematics and physics. This paper considers the nonlinear stability of boundary layer solutions for the Boltzmann equation with cutoff soft potentials when the Mach number of the far field is less than −1. Unlike the collision frequency is strictly positive in the hard potential or hard sphere model, the collision frequency has no positive lower bound for the cutoff soft potentials, so the decay in time cannot be expected. Instead, the present paper proves that the solution will always be in a small region around the boundary layer by noticing the decay property of collision operator in velocity. 相似文献
15.
牛磊 《纯粹数学与应用数学》2011,27(2):256-260
采用Kress变换以及处理第一类奇异核的积分方法,运用Nystrom方法利用单层位势求解尖角区域上的Dirichlet外问题.给出具体的算法和数值例子,通过数值例子可以看出用单层位势求解尖角区域上的Dirichlet外问题与用单双层结合求解所得的结果基本上一致,说明这种方法是有效的和可行的. 相似文献
16.
The Dirichlet problem for the Stokes equations is studied in a planar domain. We construct a solution of this problem in form of appropriate potentials and determine the unknown source densities via integral equation systems on the boundary of the domain. The solution is given explicitly in the form of a series. As a consequence we determine a solution of the Dirichlet problem for a compressible Stokes system and a solution of a boundary value problem on a domain with cracks. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
17.
We show existence and uniqueness theorem of local strong solutions to the Navier–Stokes equations with arbitrary initial data and external forces in the homogeneous Besov space with both negative and positive differential orders which is an invariant space under the change of scaling. If the initial data and external forces are small, then the local solutions can be extended globally in time. Our solutions also belong to the Serrin class in the usual Lebesgue space. The method is based on the maximal Lorentz regularity theorem of the Stokes equations in the homogeneous Besov spaces. As an application, we may handle such singular data as the Dirac measure and the single layer potential supported on the sphere. 相似文献
18.
S.M. MousaviS.J. Fariborz 《Applied Mathematical Modelling》2012,36(4):1626-1638
Stress analysis is carried out in a graded orthotropic layer containing a screw dislocation undergoing time-harmonic deformation. Energy dissipation in the layer is modeled by viscous damping. The stress fields are Cauchy singular at the location of dislocation. The dislocation solution is utilized to derive integral equations for multiple interacting cracks with any location and orientation in the layer. These equations are solved numerically thereby obtaining the dislocation density function on the crack surfaces and stress intensity factors of cracks. The dependencies of stress intensity factors of cracks on the excitation frequency of applied traction and material properties of the layer are investigated. The analysis allows the determination of natural frequencies of a cracked layer. Furthermore, the interactions of two cracks having various configurations are studied. 相似文献
19.
本文计算了环形截面的扩压通道内带进气旋绕的流动.在小横向流假定下.用三维边界层积分方程法求解内外壁面附近的流动.通过对子午面上与流线子午投影准正交方向的速度梯度方程和流量不变方程的迭代求解得出边界层外的势流场.计算与实验结果基本符合.本研究可用于分析环形扩压器内带进气予旋的流动. 相似文献