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1.
常微分方程边值问题的数值解法有多种,其中较常用的是化边值问题为初值问题解法以及边值问题差分解法.常微分方程边值问题数值解的Chebyshev谱方法是近年来出现的一种新解法.作为应用例子,分别采用Chebyshev谱方法、化边值问题为初值问题解法、以及边值问题差分解法对一类二阶常微分方程边值问题进行数值求解,并对数值解的精确性及计算时间定量地比较,从而说明Chebyshev解法是精度很高的一种快捷解法.  相似文献   

2.
本文用积分估计的方法对于一类更广泛的Захаров方程组的初边值问题(其中一维问题为第三初边值问题,二维为第一初边值问题),证明了广义解的存在性。  相似文献   

3.
借助于与给定共振的非线性周期边值问题相关的非共振的线性边值问题来构造算子,利用范数形式的锥拉伸-压缩不动点定理,得到了非线性周期边值问题非负解的存在性定理.  相似文献   

4.
研究了一类非线性三阶微分方程边值问题解的存在唯一性.首先分析了近年来国内外三阶微分方程边值问题的研究成果,提出了边值条件中含非线性函数的非线性三阶微分方程边值问题.然后寻找相关线性问题的解决途径,利用Banach不动点定理,证明了提出的边值问题存在唯一解.最后,举例阐述了主要结果的应用.  相似文献   

5.
讨论了二阶Sturm-Liouville特征值边值问题解的存在性与非存在性,得到了边值问题至少有一个正解的特征值λ的存在区间的结论.进一步,给出了边值问题没有正解的特征值存在区间.  相似文献   

6.
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   

7.
夏必腊  王金山 《大学数学》2011,27(3):120-123
首先给出了自共轭常微分方程及其边值问题,进而证明了自共轭常微分方程边值问题等价于一个泛函变分的极值问题,最后指出了将自共轭常微分方程边值问题转换为等价的泛甬变分极值问题的好处.  相似文献   

8.
本文研究了一类带有p-Laplace算子的分数阶微分方程两点边值问题.利用锥上的不动点定理,得到了这类边值问题的特征区间,推广了整数阶边值问题情形的结论.  相似文献   

9.
本文研究了一类一阶脉冲时滞积分微分方程边值问题解的性质.利用迭代分析方法,得到了该类边值问题解的存在性、唯一性和平凡解一致稳定的充分条件,推广了已有积分微分方程周期边值问题解的结论.  相似文献   

10.
利用格林函数的性质和Banach压缩映射原理讨论了含P-Laplacian算子反周期边值问题的解.首先,求出与该边值问题相关的格林函数并给出了格林函数的性质;然后将边值问题转化为与其等价的积分方程,利用格林函数的性质及Banach压缩映射原理得到边值问题解的唯一性;最后给出实例验证结果的合理性.  相似文献   

11.
装卸工问题是从现代物流技术中提出的一个实际问题,这个问题的雏形早在上个世纪60年代中国科学院数学研究所就提出和研究过.现代物流技术迅速发展,促成和推动装卸工问题的提出和研究.装卸工问题是一个新的NP困难的组合优化问题,首先介绍装卸工问题及限制情况下装卸工问题的数学模型,然后分析限制情况下的装卸工问题的性质,最后给出该问题的所有最优解.  相似文献   

12.
该文研究三种新变形的全一问题及最小全一问题. 原始的全一问题可被形象的称为顶点点亮顶点问题, 而这三类新问题则分别被称为顶点点亮边问题,边点亮顶点问题,边点亮边问题. 顶点点亮顶点问题已经得到了广泛的研究. 比如,解的存在性问题和求解的有效算法已经被解决,一般图上的最小顶点点亮顶点问题已经被证明是NP- 完备的,树、单圈图和双圈图上的最小顶点点亮顶点问题的线性时间最优算法也已被给出等. 该文对于顶点点亮边问题,证明一个图有解当且仅当它是二部图,因此只可能有两组解和最优解. 对于边点亮顶点问题,证明一个图有解当且仅当它包含偶数个顶点,并通过将其最优问题多项式变换成最小权的完美匹配问题,得出一般图上的最小边点亮顶点问题可在多项式时间内求解. 边点亮边问题可归约成线图上的顶点点亮顶点问题.  相似文献   

13.
一类双曲反问题的逼近算法及收敛性   总被引:1,自引:0,他引:1  
该文考虑地球物理勘探中出现的间断特性阻抗的反演问题.利用样条插值理论,把无穷维空间上的反问题用有限维空间上的反问题来近似.利用半群理论,证明了近似反问题之解收敛于原反问题之解.据此可得到求解反问题的一种稳定的近似算法.  相似文献   

14.
In this paper, the optimal control problem is governed by weak coupled parabolic PDEs and involves pointwise state and control constraints. We use measure theory method for solving this problem. In order to use the weak solution of problem, first problem has been transformed into measure form. This problem is reduced to a linear programming problem. Then we obtain an optimal measure which is approximated by a finite combination of atomic measures. We find piecewise-constant optimal control functions which are an approximate control for the original optimal control problem.  相似文献   

15.
M. X. You 《Applicable analysis》2018,97(9):1611-1627
In this paper, the duality theory of a generalized quasi-equilibrium problem (also called generalized Ky Fan quasi-inequality) is investigated by using the image space approach. Generalized quasi-equilibrium problem is transformed into a minimization problem. The minimization problem is further reformulated as an image problem by virtue of linear/nonlinear separation function. The dual problem of the image problem is constructed in the image space, then zero duality gap between the image problem and its dual problem is derived under saddle point condition as well as the equivalent regular linear/nonlinear separation condition. Finally, some more sufficient conditions guaranteeing zero duality gap are also proposed.  相似文献   

16.
A problem of reconstruction of boundary regimes in a model for free convection of a high-viscosity fluid is considered. A variational method and a quasi-inversion method are suggested for solving the problem in question. The variational method is based on the reduction of the original inverse problem to some equivalent variational minimum problem for an appropriate objective functional and solving this problem by a gradient method. When realizing the gradient method for finding a minimizing element of the objective functional, an iterative process actually reducing the original problem to a series of direct well-posed problems is organized. For the quasi-inversion method, the original differential model is modified by means of introducing special additional differential terms of higher order with small parameters as coefficients. The new perturbed problem is well-posed; this allows one to solve this problem by standard methods. An appropriate choice of small parameters gives an opportunity to obtain acceptable qualitative and quantitative results in solving the inverse problem. A comparison of the methods suggested for solving the inverse problem is made with the use of model examples.  相似文献   

17.
Four NP-hard optimization problems on graphs are studied: The vertex separator problem, the edge separator problem, the maximum clique problem, and the maximum independent set problem. We show that the vertex separator problem is equivalent to a continuous bilinear quadratic program. This continuous formulation is compared to known continuous quadratic programming formulations for the edge separator problem, the maximum clique problem, and the maximum independent set problem. All of these formulations, when expressed as maximization problems, are shown to follow from the convexity properties of the objective function along the edges of the feasible set. An algorithm is given which exploits the continuous formulation of the vertex separator problem to quickly compute approximate separators. Computational results are given.  相似文献   

18.
Moving men and materials in large numbers and quantities is a long-standing military problem faced by all arms. An important part of this is the routing of convoys so that they reach their correct destinations in the shortest time. The optimization problem at the heart of this problem is referred to as the convoy movement problem. Previous work on the convoy movement problem has made the assumption that the problem is difficult in practice because of the NP-hardness of the problem in combination with the limited success of early approaches based on genetic algorithms. As a result subsequent work has focused on mathematical programming-based methods, principally Lagrangian relaxation. In this paper, we demonstrate that a straightforward reformulation of the problem renders the real-world like instances, used to benchmark previous approaches, amenable to solution by simple heuristics. The main lessons learnt from this work is that analysis of the problem in conjunction with simple algorithms can, in practice, yield surprisingly effective solutions.  相似文献   

19.
In this paper, we study the uniqueness problem of a two-phase elliptic free boundary problem arising from the phase transition problem subject to given boundary data. We show that in general the comparison principle between the sub- and super-solutions does not hold, and there is no uniqueness of either a viscosity solution or a minimizer of this free boundary problem by constructing counter-examples in various cases in any dimension. In one-dimension, a bifurcation phenomenon presents and the uniqueness problem has been completely analyzed. In fact, the critical case signifies the change from uniqueness to non-uniqueness of a solution of the free boundary problem. Non-uniqueness of a solution of the free boundary problem suggests different physical stationary states caused by different processes, such as melting of ice or solidification of water, even with the same prescribed boundary data. However, we prove that a uniqueness theorem is true for the initial-boundary value problem of an ε-evolutionary problem which is the smoothed two-phase parabolic free boundary problem.  相似文献   

20.
现代物流技术中装卸工问题的拟多项式时间可解情况   总被引:10,自引:0,他引:10  
装卸工问题是从现代物流技术中提出的一个实际问题,这个问题的雏形早在上个世纪60年代中国科学院数学研究所就提出和研究过。现代物流业的迅速发展,促成和推动装卸工问题的提出和研究。装卸工问题是一个新的NP困难的组合优化问题,本文研究限制情形下的装卸工问题,并证明是拟多项式时间可解的。  相似文献   

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