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§1.引言在本文中,作者用“斯蒂阶型积分方程”方法把[1]中处理椭圆型方程的狄利克雷问题与牛孟问题的弗雷特霍姆积分方程法推广到具有不连续边界条件的情形,研究了“广义狄利克雷问题”与“广义牛孟问题”,即求m维空间的有界区域Ω上方程(1)的正规解u(p),并在Ω的边界 相似文献
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通过研究狄利克雷核的一般性质,讨论P-级数域重排特征系统的加权极大狄利克雷核函数的积分情况,并给出加权极大函数可积的充要条件. 相似文献
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本文讨论了在实轴上具有紧支集的势的薛定谔算子的极点散射问题. 本文旨在将狄利克雷级数理论与散射理论相结合, 文中运用了Littlewood的经典方法得到关于极点个数的新的估计. 本文首次将狄利克雷级数方法用于极点估计, 由此得到了极点个数的上界与下界, 这些结果改进和推广了该论题的一些相关结论. 相似文献
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Engel群是次黎曼几何中的一类重要的单连通幂零李群.本文研究了Engel群E=(R4,■,{δλ})的有界区域Ω上次Laplace算子△E的狄利克雷特征值问题■其中v是边界?Ω的单位外法向量场.我们建立了该问题的一些万有特征值不等式. 相似文献
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《应用泛函分析学报》2016,(3)
通过使用叠合度理论、M-矩阵、李雅谱诺夫函数和不等式技巧等,在时间尺度上研究带有狄利克雷边值和反应扩散项的非自治模糊细胞神经网络的全局指数稳定性,并获得一些使其存在全局指数稳定的平衡点的充分条件.最后,给出一个例子去验证结论的有效性. 相似文献
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<正> 本文着重讨论了拉普拉斯变换中的两个问题,一个是关于拉普拉斯变换的概念,另一个是关于初值定理与终值定理。1 拉普拉斯普换概念1.拉普拉斯变换定义:在富氏变换存在定理中,不仅要求函数f(t)在任一有限区间上满足狄利克雷条件,且还要求它在(-∞, 相似文献
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Abdon Atangana 《Journal of Applied Analysis & Computation》2015,5(3):273-283
The work presents an adaptation of iteration method for solving a class of thirst order partial nonlinear differential equation with mixed derivatives.The class of partial differential equations present here is not solvable with neither the method of Green function, the most usual iteration methods for instance variational iteration method, homotopy perturbation method and Adomian decomposition method, nor integral transform for instance Laplace,Sumudu, Fourier and Mellin transform. We presented the stability and convergence of the used method for solving this class of nonlinear chaotic equations.Using the proposed method, we obtained exact solutions to this kind of equations. 相似文献
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The group analysis method is applied to the extended Green–Naghdi equations. The equations are studied in the Eulerian and Lagrangian coordinates. The complete group classification of the equations is provided. The derived Lie symmetries are used to reduce the equations to ordinary differential equations. For solving the ordinary differential equations the Runge–Kutta methods were applied. Comparisons between solutions of the Green–Naghdi equations and the extended Green–Naghdi equations are given. 相似文献
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In this paper, we present an efficient numerical algorithm for solving a general class of nonlinear singular boundary value problems. This present algorithm is based on the Adomian decomposition method (ADM) and Green’s function. The method depends on constructing Green’s function before establishing the recursive scheme. In contrast to the existing recursive schemes based on ADM, the proposed numerical algorithm avoids solving a sequence of transcendental equations for the undetermined coefficients. The approximate series solution is calculated in the form of series with easily computable components. Moreover, the convergence analysis and error estimation of the proposed method is given. Furthermore, the numerical examples are included to demonstrate the accuracy, applicability, and generality of the proposed scheme. The numerical results reveal that the proposed method is very effective. 相似文献
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This paper deals with the solutions of linear inhomogeneous time-fractional partial differential equations in applied mathematics and fluid mechanics. The fractional derivatives are described in the Caputo sense. The fractional Green function method is used to obtain solutions for time-fractional wave equation, linearized time-fractional Burgers equation, and linear time-fractional KdV equation. The new approach introduces a promising tool for solving fractional partial differential equations. 相似文献
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L. A. Alexeyeva G. K. Zakir’yanova 《Computational Mathematics and Mathematical Physics》2011,51(7):1194-1207
The method of boundary integral equations is developed as applied to initial-boundary value problems for strictly hyperbolic
systems of second-order equations characteristic of anisotropic media dynamics. Based on the theory of distributions (generalized
functions), solutions are constructed in the space of generalized functions followed by passing to integral representations
and classical solutions. Solutions are considered in the class of singular functions with discontinuous derivatives, which
are typical of physical problems describing shock waves. The uniqueness of the solutions to the initial-boundary value problems
is proved under certain smoothness conditions imposed on the boundary functions. The Green’s matrix of the system and new
fundamental matrices based on it are used to derive integral analogues of the Gauss, Kirchhoff, and Green formulas for solutions
and solving singular boundary integral equations. 相似文献
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N. M. Plakida 《Theoretical and Mathematical Physics》2013,174(2):273-283
We consider a microscopic theory of the strong coupling in multiband superconductors with an arbitrary electron-boson interaction. Based on the method of the equations of motion for two-time Green’s functions, we derive the Dyson equation with the self-energy operator in the form of the multiparticle Green’s function taking the interaction of electrons with phonons and spin fluctuations into account. We obtain a self-consistent system of equations for the normal and anomalous components of the Green’s function and the self-energy operator calculated in the approximation of noncrossing diagrams. We discuss the approximate solution of the system of equations taking only components of the self-energy operator that are diagonal with respect to the band index into account for studying superconductivity in iron-based compounds. 相似文献
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Randhir Singh Jitendra Kumar Gnaneshwar Nelakanti 《Journal of Applied Mathematics and Computing》2013,43(1-2):409-425
In this work, an effective technique for solving a class of singular two point boundary value problems is proposed. This technique is based on the Adomian decomposition method (ADM) and Green’s function. The technique relies on constructing Green’s function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on ADM, the proposed recursive scheme avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. For the completeness, the convergence and error analysis of the proposed scheme is supplemented. Moreover, the numerical examples are included to demonstrate the accuracy, applicability, and generality of the proposed scheme. The results reveal that the method is very effective, straightforward, and simple. 相似文献
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We develop the theory of quantum transport of electrons through systems with strong correlations between fermionic and internal spin degrees of freedom. The atomic representation for the Hamiltonian of a device and nonequilibrium Green’s functions constructed using the Hubbard operators allow overcoming difficulties in the perturbation theory encountered in the traditional approach because of a larger number of bare scattering amplitudes. Representing the matrix elements of effective interactions as a superposition of terms each of which is split in matrix indices, we obtain a simple method for solving systems of very many equations for nonequilibrium Green’s functions in the atomic representation. As a result, we obtain an expression describing the electron currents in a device one of whose sites is in tunnel coupling with the left contact and the other, with the right contact. We derive closed kinetic equations for the occupation numbers under conditions where the electron flow leads to significant renormalization of them. 相似文献
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Separation of variables is a well‐known technique for solving differential equations. However, it is seldom used in practical applications since it is impossible to carry out a separation of variables in most cases. In this paper, we propose the amplitude–shape approximation (ASA) which may be considered as an extension of the separation of variables method for ordinary differential equations. The main idea of the ASA is to write the solution as a product of an amplitude function and a shape function, both depending on time, and may be viewed as an incomplete separation of variables. In fact, it will be seen that such a separation exists naturally when the method of lines is used to solve certain classes of coupled partial differential equations. We derive new conditions which may be used to solve the shape equations directly and present a numerical algorithm for solving the resulting system of ordinary differential equations for the amplitude functions. Alternatively, we propose a numerical method, similar to the well‐established exponential time differencing method, for solving the shape equations. We consider stability conditions for the specific case corresponding to the explicit Euler method. We also consider a generalization of the method for solving systems of coupled partial differential equations. Finally, we consider the simple reaction diffusion equation and a numerical example from chemical kinetics to demonstrate the effectiveness of the method. The ASA results in far superior numerical results when the relative errors are compared to the separation of variables method. Furthermore, the method leads to a reduction in CPU time as compared to using the Rosenbrock semi‐implicit method for solving a stiff system of ordinary differential equations resulting from a method of lines solution of a coupled pair of partial differential equations. The present amplitude–shape method is a simplified version of previous ones due to the use of a linear approximation to the time dependence of the shape function. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献