共查询到20条相似文献,搜索用时 78 毫秒
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本文刻画了常型Sturm-Liouville问题的左定空间的一般形式.根据自伴边值条件的分类,确切地给出了所有可能的左定空间描述. 相似文献
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应用左定和定型Sturm-Liouville问题特征值的Prüfer角刻画,以及其特征值对边界和边值条件的单调依赖关系,本文建立了左定Sturm-Liouville与两个相关的定型Sturm-Liouville问题之间的特征值不等式关系. 相似文献
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一类两边界条件含参数的Sturm-Liouville问题 总被引:1,自引:0,他引:1
考虑第一个边界条件为参数的线性函数,第二个边界条件为有理函数的Sturm-Liouville问题.给出问题的特征值、特征函数的渐近式以及特征函数的振荡理论,并给出相应的应用实例. 相似文献
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利用左定微分算子与相应的右定微分算子之间的关系来研究左定微分算子.首先给出四阶奇异微分算子的自共轭域;接着利用主解与Friedrichs扩张寻找最小算子的正的自共轭扩张;最后通过系数、区间端点和边界条件给出四阶奇异微分算子左定性的充要条件以及相应的左定边值矩阵的情形. 相似文献
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研究了一类内部具有无穷多个不连续点的Sturm-Liouville问题,即内部具有无穷多个转移条件的Sturm-Liouville问题.把此类问题放到一个新的空间中去考虑,定义了与转移条件相关联的最小算子Cmin和最大算子Cmax,给出了最小算子Cmin是下有界的一个充分条件,进一步由边界条件刻画了具有下有界的最小算子Cmin的Friedrichs扩张. 相似文献
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研究了一端奇异且在内部具有转移条件的Sturm-Liouville算子的Weyl函数,我们给出了相应的Weyl函数的定义,并对Weyl函数性质进行了讨论. 相似文献
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本文在与边界条件有关的修正Hilbert空间中考察一类边界条件含谱参数并具有转移条件的Sturm-Liouville问题.得到了λ为该问题特征值的等价条件,给出了该问题的格林函数. 相似文献
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Rainer Glüge 《PAMM》2013,13(1):251-252
We discuss generalized boundary conditions for representative volume elements (RVE), which include the classical boundary conditions as special cases. From the generalization, stochastic boundary conditions are derived. These allows to adjust the the stiffness of the boundary conditions smoothly between the extremal cases of homogeneous strain and homogeneous stress boundary conditions. We found that it needs to be distinguished between the resistance of the boundary conditions against homogeneous and inhomogeneous RVE deformation. The stochastic BC can combine the moderate stiffness of the well known periodic boundary conditions with the high resistance against localization of the homogeneous strain boundary conditions. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Duffing型方程组的边界值问题的解的存在性 总被引:5,自引:0,他引:5
给出了带Dirichlet边界条件、Neumann边界条件和周期边界条件的Duffing型方程组的两点边界值问题的解的几个存在性定理。 相似文献
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A. M. Akhtyamov 《Differential Equations》2017,53(11):1515-1518
We describe all degenerate two-point boundary conditions possible in a homogeneous spectral problem for the diffusion operator. We show that the case in which the characteristic determinant is identically zero is impossible for the nonsymmetric diffusion operator and that the only possible degenerate boundary conditions are the Cauchy conditions. For the symmetric diffusion operator, the characteristic determinant is zero if and only if the boundary conditions are falsely periodic boundary conditions; the characteristic determinant is identically a nonzero constant if and only if the boundary conditions are generalized Cauchy conditions. 相似文献
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In this paper we are concerned with the initial boundary value problem for the micropolar fluid system in nonsmooth domains with mixed boundary conditions. The considered boundary conditions are of two types: Navier’s slip conditions on solid surfaces and Neumann-type boundary conditions on free surfaces. The Dirichlet boundary condition for the microrotation of the fluid is commonly used in practice. However, the well-posedness of problems with different types of boundary conditions for microrotation are completely unexplored. The present paper is devoted to the proof of the existence, regularity and uniqueness of the solution in distribution spaces. 相似文献
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S.M Roberts 《Journal of Mathematical Analysis and Applications》1980,77(1):73-99
The Kagiwada-Kalaba method of invariant imbedding for multidimensional systems is first derived for the split linear implicit boundary conditions. The justification for the Kagiwada-Kalaba procedure is explained in terms of the special nature of the split linear implicit boundary conditions. Extension of the Kagiwada-Kalaba method from the split linear implicit boundary conditions to general linear implicit boundary conditions is described. 相似文献
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《Applied Mathematics Letters》2006,19(8):735-740
We introduce new boundary conditions for large eddy simulation. These boundary conditions are based on an approximate deconvolution approach. They are computationally efficient and general, which makes them appropriate for the numerical simulation of turbulent flows with time-dependent boundary conditions. Numerical results are presented to demonstrate the new boundary conditions in a simplified linear setting. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(9):3495-3508
We study matrix representations of Sturm‐Liouville problems with coupled eigenparameter‐dependent boundary conditions and transmission conditions. Meanwhile, given any matrix eigenvalue problem with coupled eigenparameter‐dependent boundary conditions and transmission conditions, we construct a class of Sturm‐Liouville problems with given boundary conditions and transmission conditions such that they have the same eigenvalues. 相似文献
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Ventcel boundary conditions are second order differential conditions that appear in asymptotic models. Like Robin boundary conditions, they lead to well-posed variational problems under a sign condition of the coefficient. This is achieved when physical situations are considered. Nevertheless, situations where this condition is violated appeared in several recent works where absorbing boundary conditions or equivalent boundary conditions on rough surfaces are sought for numerical purposes. The well-posedness of such problems was recently investigated: up to a countable set of parameters, existence and uniqueness of the solution for the Ventcel boundary value problem holds without the sign condition. However, the values to be avoided depend on the domain where the boundary value problem is set. In this work, we address the question of the persistency of the solvability of the boundary value problem under domain deformation. 相似文献
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Spatial pattern formations in diffusive predator-prey systems with non-homogeneous Dirichlet boundary conditions 下载免费PDF全文
A reaction-diffusion predator-prey system with non-homogeneous Dirichlet boundary conditions describes the persistence of predator and prey species on the boundary. Compared with homogeneous Neumann boundary conditions, the former conditions may prompt or prevent the spatial patterns produced through diffusion-induced instability. The spatial pattern formation induced by non-homogeneous Dirichlet boundary conditions is characterized by the Turing type linear instability of homogeneous state and bifurcation theory. Furthermore, transient spatiotemporal behaviors are observed through numerical simulations. 相似文献
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In this paper we consider boundary value problems in perforated domains with periodic structures and cavities of different scales, with the Neumann condition on some of them and mixed boundary conditions on others. We take a case when cavities with mixed boundary conditions have so called critical size (see [1]) and cavities with the Neumann conditions have the scale of the cell. In the same way other cases can be studied, when we have the Neumann and the Dirichlet boundary conditions or the Dirichlet condition and the mixed boundary condition on the boundary of cavities.There is a large literature where homogenization problems in perforated domains were studied [2];-[7]; 相似文献