共查询到19条相似文献,搜索用时 78 毫秒
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利用变分法证明平面调和函数的外问题的确切形式;在此基础上,建立外问题的具有间接变量的等价边界积分方程;传统的外问题及边界积分方程不具有普遍适用性,本文对此进行了详细的讨论. 相似文献
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声波的散射问题中,如果散射体由不可穿透障碍物和可穿透裂缝两部分组成,障碍物表面分别满足第一类和第三类边界条件,裂缝两边满足不同的第二类边界条件,通过位势理论,可以将此混合问题转化为边界积分方程,通过Fredholm算子理论可以得到这个边界积分方程解的存在性和唯一性,从而获得原问题解的存在和唯一性. 相似文献
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本文发现,以往习用的平面调和函数的两种边界积分方程不是充要的,其原因是一个实际上并不能包括全部调和函数的边界积分表达式误解为能如此.本文改正了这个表达式,并进而导出了充要的直接变量和间接变量的边界积分方程 相似文献
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本文对两个非均匀半平面粘结的非均匀平面的裂纹问题作了分析,文中假定两种材料的泊松比v相同,但杨氏模量随坐标x按不同形式的指数函数变化.本文使用非均匀平面问题的单裂纹解及富氏变换方法, 使问题归为一个柯西型奇异积分方程,最后对应力强度因子的计算给出了若干数值例子. 相似文献
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讨论了浅海中波导的声波散射问题,我们将该问题归结为一个第一类边界积分方程,利用正同化方法求解,并证明了该方法的收敛性,数值例子表明了该方法的简单与有效性。 相似文献
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In this paper we consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open arc in R2 as the cross section. We assume that the arc is divided into two parts, and one of the two parts is (possibly) coated on one side by a material with surface impedance λ. Applying potential theory, the problem can be reformulated as a boundary integral system. We obtain the existence and uniqueness of a solution to the system by using Fredholm theory. 相似文献
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In this paper we consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open arc and a bounded domain in R2 as cross section. To this end, we solve a scattering problem for the Helmholtz equation in R2 where the scattering object is a combination of a crack Γ and a bounded obstacle D, and we have Dirichlet-impedance type boundary condition on Γ and Dirichlet boundary condition on ∂D (∂D∈C2). Applying potential theory, the problem can be reformulated as a boundary integral system. We establish the existence and uniqueness of a solution to the system by using the Fredholm theory. 相似文献
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Simon N. Chandler-Wilde Christopher R. Ross 《Mathematical Methods in the Applied Sciences》1996,19(12):959-976
We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained. 相似文献
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本文讨论了确定Laplitce双曲型方程uxy(x,y)+a(x,y)ux(x,y)+b(x,y)+uy(x,y)+q(x)u(x,y)=f(x,y)的广义Cauchy问题中系数q(x)的反问题。文中利用特征法线及不动点理论,导出了与反问题等价的非线性积分方程组,证明了反问题局部解的存在唯一性,最后给出了反问题整体用的唯一性定理。 相似文献
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程建纲 《数学物理学报(A辑)》2005,25(4):482-488
该文考虑两点边值问题[1/q(t)][q(t)y′(t)]′+p(t)f(y(t))= 0,λ_1 y(α)-λ_2y′(α)=0 and y(β)=B非负解的存在性, 其中p(t)可能在t=α或t=β附近具有奇异性, f(0)≥0,
lim_(y→+∞)f(y)/y=+∞, 并且存在y>0, 使得f(y)<0. 相似文献
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运用Schauder不动点定理,考察了边值问题Δ4u(k-1)=g(k,u(k-1),u(k),u(k 1),u(k 2)),k∈Z(1,N)u(0)=A,u(N 1)=B,u(N 2)=C,u(N 3)=D解的存在性. 相似文献
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In this paper we study the existence of solution for the following Cauchy problem {u_t = Δu^m - u^p u(x,0) = u_0(x) We show how the growth condition of initial trace is determined by the absorption. 相似文献
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Existence and Uniqueness of Solutions for the Initial Value Problem of Fractional $q_{k}$-Difference Equations for Impulsive with Varying Orders 下载免费PDF全文
The paper studies the existence and uniqueness for impulsive fractional $q_{k}$-difference equations of initial value problems involving Riemann-Liouville fractional $q_{k}$-integral and $q_{k}$-derivative by defining a new $q$-shifting operator. In this paper, we obtain existence and uniqueness results for impulsive fractional $q_{k}$-difference equations of initial value problems by using the Schaefer''s fixed point theorem and Banach contraction mapping principle. In addition, the main result is illustrated with the aid of several examples. 相似文献
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本文讨论具有抛物边界层的半线性抛物型方程奇异摄动问题的数值解法,在非均匀网格上构造了两层非线性差分格式,证明了差分格式是一致收敛的,给出了一些数值例子. 相似文献