共查询到20条相似文献,搜索用时 10 毫秒
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E. H. Khalilov 《Differential Equations》2018,54(4):539-550
We substantiate the collocation method for the singular integral equation of a boundary value problem with impedance condition for the Helmholtz equation. We construct a sequence converging to the exact solution of the original problem and estimate the error. 相似文献
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Doklady Mathematics - The collocation method is justified for the integral equation of the impedance boundary value problem for the Helmholtz equation. A sequence is constructed that converges to... 相似文献
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P.A. Krutitskii 《Applicable analysis》2013,92(1):69-83
We propose an approach for reduction of the impedance problem for propagative Helmholtz equation outside several obstacles to the uniquely solvable Fredholm integral equation of the second kind and index zero. The integral equation in this approach is derived by introducing auxiliary boundaries with an appropriate boundary conditions inside obstacles. 相似文献
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Problems for electromagnetic scattering are of significant importance in many areas of technology. In this paper we discuss the scattering problem of electromagnetic wave incident by using boundary element method associated with splines. The problem is modelled by a boundary value problem for the Helmholtz eouation 相似文献
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The main objective is the study of a class of boundary value problems in weak formulation where two boundary conditions are
given on the half-lines bordering the first quadrant that contain impedance data and oblique derivatives. The associated operators
are reduced by matricial coupling relations to certain boundary pseudodifferential operators which can be analyzed in detail.
Results are: Fredholm criteria, explicit construction of generalized inverses in Bessel potential spaces, eventually after
normalization, and regularity results. Particular interest is devoted to the impedance problem and to the oblique derivative
problem, as well. 相似文献
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Zhang Kang-qun 《数学研究通讯:英文版》2019,35(1)
Fundamental solution of Dirichlet boundary value problem of axisymmetric Helmholtz equation is constructed via modi?ed Bessel function of the second kind, which uni?ed the formulas of fundamental solution of Helmholtz equation, elliptic type Euler-Poisson-Darboux equation and Laplace equation in any dimensional space. 相似文献
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We consider a class of boundary value problems for the three-dimensional Helmholtz equation that appears in diffraction theory.
On the three faces of the octant, which are quadrants, we admit first order boundary conditions with constant coefficients,
linear combinations of Dirichlet, Neumann, impedance and/or oblique derivative type. A new variety of surface potentials yields
3 × 3 boundary pseudodifferential operators on the quarterplane that are equivalent to the operators associated to the boundary value problems in a Sobolev space setting. These operators
are analyzed and inverted in particular cases, which gives us the analytical solution of a number of well-posed problems.
Dedicated to Vladimir G. Maz’ya on the occasion of his 70th birthday 相似文献
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Doklady Mathematics - Within the framework of the theory of operator cosine functions and its application, a solution of the Dirichlet boundary value problem for the generalized Helmholtz equation... 相似文献
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关于Helmholtz外问题的边界积分方程解的唯一性问题 总被引:4,自引:0,他引:4
本文用能量分析的观点探讨了用边界积分方程描述Helmholtz外问题时,解的唯一性不能保持的原因.文中证明了,当利用积分方程来描述问题时,实际上将无穷远处的Sommerfeld条件改成了既适合于外向波(辐射波),又适合于内向波(吸收波),即整个系统的能量保持守恒.并根据此观点解释了保持唯一性的算法. 相似文献
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We discuss a method for seeking integrable boundary conditions for nonlinear equations. For the Boussinesq equation, we find a new boundary condition that is compatible with the Lax pair and has an infinite set of higher symmetries and a Bäcklund transformation. We construct a class of explicit partial solutions of an equation satisfying this boundary condition. 相似文献
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本文考虑多柱域上非齐次的Cauchy-Riemann方程的Riemann-Hilbert边值问题.讨论了上述边值问题可解的充分必要条件,并给出了边值问题解的积分表达式. 相似文献
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曹丽霞 《数学的实践与认识》2011,41(24)
给出了边界过原点的任意半平面中的Hilbert边值问题的提法,定义了函数的一种对称扩张,并利用这种对称扩张将此Hilbert边值问题转化为无穷直线上的Riemann边值问题,得到了该问题的一般解和可解性定理. 相似文献
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In this paper, we study a system of biharmonic equations coupled by the boundary conditions. These boundary conditions contain some combinations of the values, div, curl, and grad. Applications in mathematical physics are possible and the investigations will be done with the help of hypercomplex methods. It is also the aim of the paper to demonstrate the application of Clifford analytic methods to the solution of boundary value problems. The results on a special boundary value problem for the biharmonic equation will be used for the investigation of some first-order systems of partial differential equations. We study a theoretical problem connected with the ∂¯-problem and the solution of a Beltrami system by using a fixed-point iteration. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
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李玉成 《数学物理学报(A辑)》2000,20(2):235-239
该文考虑方程组
t(ux - vy - wt ) + w = 0 (H)
uy = -vx, ut = -wx, vt = wy
的解f = u + iv + jt ∈C2,找到(H)可解的一个充要条件,并讨论相关边值问题解的存在性和积分表示,推广了1992年H. Leutwiler[1]的结果. 相似文献
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Moscow University Computational Mathematics and Cybernetics - A case is considered in which when the solution to the boundary value problem for a third-order singularly perturbed ordinary... 相似文献
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