共查询到20条相似文献,搜索用时 15 毫秒
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In this article we consider the inverse coefficient problem of recovering the function { ( x ) system of partial differential equations that can be reduced to a second order integro-differential equation $ -u_{xx} + c(x)u_{x} + d\phi (x)u-\gamma d\phi (x)\int _{0}^{t}e^{-\gamma (t-\tau )}u(x,\tau )\, d\tau = 0 $ with boundary conditions. We prove the existence and uniqueness of solutions to the inverse problem and develop a numerical algorithm for solving this problem. Computational results for some examples are presented. 相似文献
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研究了奇型Sturm-Liouville算子的逆问题.对于固定的n∈N,证明了Sturm-Liouville问题(1.3)-(1.5)的第n个特征值λ_n(q,H)关于H是严格单调增加的,及一组不同边界条件下的第n个特征值的谱集合{λ_n(q,H_k)}_(k=1)~(+∞)能够唯一确定(0,πr)上的势函数q(x). 相似文献
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Robert Carlson 《Journal of Mathematical Analysis and Applications》2002,267(2):564-575
By modifying and generalizing some old techniques of N. Levinson, a uniqueness theorem is established for an inverse problem related to periodic and Sturm-Liouville boundary value problems for the matrix Schrödinger equation. 相似文献
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根据热方程的正问题理论,建立了一个联系附加数据和未知源项的积分恒等式并据此证明了非线性源项的存在唯一性. 相似文献
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逆结点问题是通过特征函数的零点重构算子.
本文主要讨论具有特征参数多项式边界条件的 Sturm-Liouville 方程的逆结点问题.
20世纪50年代以后,人们发现在许多工程领域, Sturm-Liouville 问题的谱参数不仅出现在方程中,
而且也出现在边界条件中,因此带参数边界条件的逆结点问题对数学物理方面的研究有重要意义.
本文讨论区间 $[0,1]$ 上边界条件为参数多项式的 Sturm-Liouville 方程的逆结点问题,
并证明在 $[0,b]$ \big($ b\in \big(\frac{1}{2},1\big]$\big) 上结点的稠密子集可唯一确定 $[0,1]$ 上的势函数和边界条件中多项式的未知系数. 相似文献
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讨论确定Sturm-Liouville问题中算子的系数α(x)或者q(x)的问题.在一定条件下,系数α(x)或者q(x)可由数据或者数据唯一确定,这里的uj(x)满足而构成L2(0,1)的一个基,α和β为给定的实数. 相似文献
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Lauri Oksanen 《偏微分方程通讯》2013,38(9):1492-1518
We consider boundary measurements for the wave equation on a bounded domain M ? ?2 or on a compact Riemannian surface, and introduce a method to locate a discontinuity in the wave speed. Assuming that the wave speed consist of an inclusion in a known smooth background, the method can determine the distance from any boundary point to the inclusion. In the case of a known constant background wave speed, the method reconstructs a set contained in the convex hull of the inclusion and containing the inclusion. Even if the background wave speed is unknown, the method can reconstruct the distance from each boundary point to the inclusion assuming that the Riemannian metric tensor determined by the wave speed gives simple geometry in M. The method is based on reconstruction of volumes of domains of influence by solving a sequence of linear equations. For τ ∈C(?M) the domain of influence M(τ) is the set of those points on the manifold from which the distance to some boundary point x is less than τ(x). 相似文献
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考虑了具有耦合转移条件Sturm-Liouville(简称S-L)问题的逆问题,在一定条件下,通过利用S-L方程右边的函数f_j(x)确定方程的解,并由数据{u_j(x_0)}_j~∞=i或{p(x_0)(du_j(x_0))-(dx)}_j~∞=1唯一确定S-L算子中的系数p(x)和q(x).其中u_j(x)满足S-L方程,分离边界条件和耦合转移条件,而{f_j(x)}_(j-i)~∞构成L~2(I)的一个基. 相似文献
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Journal of Applied and Industrial Mathematics - We construct a numerical method for recovering a variable coefficient in the Cauchy problem and also in the initial boundary value problem for the... 相似文献
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Guo-Qiang He & Y. M. Chen 《计算数学(英文版)》1993,11(2):103-112
In this paper the Generalized Pulse-Spectrum Technique (GPST) is extended to solve an inverse problem for the Burgers equation. We prove that the GPST is equivalent in some sense to the Newton-Kantorovich iteration method. A feasible numerical implementation is presented in the paper and some examples are executed. The numerical results show that this procedure works quite well. 相似文献
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一类特殊矩阵的逆特征值问题 总被引:9,自引:0,他引:9
本文主要讨论如下形式矩阵的逆特征值问题:即对给定n个实数λ_1>λ_2>…>λ_2与n-1个实数μ_1>μ_2>…>μ_(n-1),满足λ_1>μ_1>λ_2>…>λ_(n-1)>μ_(n-1)>λ_n,在α_2>α_3>…>α_(n-1)的条件下,存在唯一的一个矩阵A_n是以λ_i为其特征值;且其截边矩阵的特征值为μ_1,μ_2,…,μ_(n-1). 相似文献
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在[1]里已经讨论了如何根据光子密度n(x,u)(实验测得),得到总截面σ(x)的近似值,本文利用最小二乘法讨论如何通过n次观测求得σ(x)的近似值. 相似文献
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M. I. Ivanchov 《Ukrainian Mathematical Journal》2003,55(7):1086-1098
We establish conditions for the existence and uniqueness of a solution of the inverse problem for a one-dimensional heat equation with unknown time-dependent leading coefficient in the case where a part of the boundary of the domain is unknown. 相似文献
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