共查询到20条相似文献,搜索用时 394 毫秒
1.
The uniqueness of both the inverse boundary value problem and inverse scattering problem for Dirac equation with a magnetic potential and an electrical potential are proved. Also, a relation between the Dirichlet to Dirichlet map for the inverse boundary value problem and the scattering amplitude for the inverse scattering problem is given 相似文献
2.
彭秋艳 《数学的实践与认识》2005,35(9):216-220
讨论了一维波动方程系数反演的一种求解方法,将解进行一阶渐进展开,得到相应的反问题,将其转化为第二类Volttera型积分方程组,证明了反问题解的存在唯一性. 相似文献
3.
N. I. Berezina V. I. Dmitriev N. A. Mershchikova 《Computational Mathematics and Modeling》2011,22(3):229-237
The article presents a quasi-one-dimensional method for solving the inverse problem of electromagnetic sounding. The quasi-one-dimensional
method is an iteration process that in each iteration solves a parametric one-dimensional inverse problem and a two-dimensional
direct problem. The solution results of these problems are applied to update the input values for the parametric one-dimensional
inverse problem in the next iteration. The method has been implemented for a two-dimensional inverse problem of magnetotelluric
sounding in a quasi-layered medium. 相似文献
4.
杨晓光 《高校应用数学学报(英文版)》2001,16(2):185-194
Abstract. In this paper,a new model for inverse network flow problems,robust partial inverseproblem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such that all full solutions containing the partial solution becomeoptimal under new coefficients. It has been shown that the robust partial inverse spanning treeproblem can be formulated as a combinatorial linear program,while the robust partial inverseminimum cut problem and the robust partial inverse assignment problem can be solved by combinatorial strongly polynomial algorithms. 相似文献
5.
V. Yurko 《Applicable analysis》2013,92(1-2):63-77
The inverse spectral problem of recovering pencils of second-order differential operators on the half-line is studied. We give a formulation of the inverse problem, prove the uniqueness theorem and provided a procedure for constructing the solution of the inverse problem. We also establishe connections with inverse problems for partial differential equations. 相似文献
6.
Natalia P. Bondarenko 《Mathematical Methods in the Applied Sciences》2020,43(11):7009-7021
The paper deals with the Sturm–Liouville eigenvalue problem with the Dirichlet boundary condition at one end of the interval and with the boundary condition containing entire functions of the spectral parameter at the other end. We study the inverse problem, which consists in recovering the potential from a part of the spectrum. This inverse problem generalizes partial inverse problems on finite intervals and on graphs and also the inverse transmission eigenvalue problem. We obtain sufficient conditions for global solvability of the studied inverse problem, which prove its local solvability and stability. In addition, application of our main results to the partial inverse Sturm–Liouville problem on the star-shaped graph is provided. 相似文献
7.
In this paper, we consider two types of inverse sorting problems. The first type is an inverse sorting problem by minimizing
the total weighted number of changes with bound constraints. We present an O(n
2) time algorithm to solve the problem. The second type is a partial inverse sorting problem and a variant of the partial inverse
sorting problem. We show that both the partial inverse sorting problem and the variant can be solved by a combination of a
sorting problem and an inverse sorting problem.
Supported by the Hong Kong Universities Grant Council (CERG CITYU 103105) and the National Key Research and Development Program
of China (2002CB312004) and the National Natural Science Foundation of China (700221001, 70425004). 相似文献
8.
Wen-Hua Yu 《计算数学(英文版)》1993,11(2):142-153
In the paper, we first deduce an optimization problem from an inverse problem for a general operator equation and prove that the optimization problem possesses a unique, stable solution that converges to the solution of the original inverse problem, if it exists, as a regularization factor goes to zero. Secondly, we apply the above results to an inverse problem determining the spatially varying coefficients of a second order hyperbolic equation and obtain a necessary condition, which can be used to get an approximate solution to the inverse problem. 相似文献
9.
A. Yu. Shcheglov 《Computational Mathematics and Mathematical Physics》2006,46(4):616-635
The inverse problem of recovering a solution-dependent coefficient multiplying the lowest derivative in a hyperbolic equation is investigated. As overdetermination is required in the inverse problem, an additional condition is imposed on the solution to the equation with a fixed value of the timelike variable. Global uniqueness and local existence theorems are proved for the solution to the inverse problem. An iterative method is proposed for solving the inverse problem. 相似文献
10.
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
11.
12.
Given a feasible solution, the inverse optimization problem is to modify some parameters of the original problem as little as possible, and sometimes also with bound restrictions on these adjustments, to make the feasible solution become an optimal solution under the new parameter values. So far it is unknown that for a problem which is solvable in polynomial time, whether its inverse problem is also solvable in polynomial time. In this note we answer this question by considering the inverse center location problem and show that even though the original problem is polynomially solvable, its inverse problem is NP–hard. 相似文献
13.
Yashar T. Mehraliyev He Yang Elvin I. Azizbayov 《Mathematical Methods in the Applied Sciences》2023,46(2):1723-1739
In this paper, an inverse boundary value problem for a two-dimensional hyperbolic equation with overdetermination conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary value problem and prove its equivalence to the original problem in a certain sense. We then use the Fourier method to reduce such an equivalent problem to a system of integral equations. Furthermore, we prove the existence and uniqueness theorem for the auxiliary problem by the contraction mappings principle. Based on the equivalency of these problems, the existence and uniqueness theorem for the classical solution of the original inverse problem is proved. Some discussions on the numerical solutions for this inverse problem are presented including some numerical examples. 相似文献
14.
V. Yurko 《Journal of Mathematical Analysis and Applications》2006,320(1):439-463
The inverse spectral problem of recovering pencils of second-order differential operators on the half-line with turning points is studied. We establish properties of the spectral characteristics, give a formulation of the inverse problem, prove a uniqueness theorem and provide a constructive procedure for the solution of the inverse problem. 相似文献
15.
K. B. Sabitov 《Differential Equations》2011,47(5):706-714
For a third-order differential equation of parabolic-hyperbolic type, we suggest a method for studying the first boundary
value problem by solving an inverse problem for a second-order equation of mixed type with unknown right-hand side. We obtain
a uniqueness criterion for the solution of the inverse problem. The solution of the inverse problem and the Dirichlet problem
for the original equation is constructed in the form of the sum of a Fourier series. 相似文献
16.
We study the nonlinear inverse problem of estimating stochastic parameters in the fourth-order partial differential equation with random data. The primary focus is on developing a novel stochastic approximation framework for inverse problems consisting of three key components. As a first step, we reformulate the inverse problem into a stochastic convex optimization problem. The second step includes developing a new regularized stochastic extragradient framework for a nonlinear variational inequality, which subsumes the optimality conditions for the optimization formulation of the inverse problem. The third step involves modeling random variables by a Karhunen–Loève type finite-dimensional noise representation, allowing the direct and the inverse problems to be conveniently discretized. We show that the regularized extragradient methods are strongly convergent in a Hilbert space setting, and we also provide several auxiliary results for the inverse problem, including Lipschitz continuity and a derivative characterization of the solution map. We provide the outcome of computational experiments to estimate stochastic and deterministic parameters. The numerical results demonstrate the feasibility and effectiveness of the developed framework and validate stochastic approximation as an effective method for stochastic inverse problems. 相似文献
17.
An inverse source problem for the wave equation with additional information measured on some parts of the boundary is considered. The degree of ill-posedness of the inverse problem is investigated. A numerical algorithm based on the SVD of a discrete inverse problem is constructed and tested. 相似文献
18.
Fahir Talay Akyildiz Salih Tatar Suleyman Ulusoy 《Mathematical Methods in the Applied Sciences》2013,36(17):2397-2402
This paper analyzes the existence and the uniqueness problem for an n‐dimensional nonlinear inverse reaction‐diffusion problem with a nonlinear source. A transformation is used to obtain a new inverse coefficient problem. Then, a parabolic differential operator Lλ is defined to establish the relation between the solution of Lλ = 0 and the new inverse problem. Following this, it is shown that the inverse problem has at least one solution in the class of admissible coefficients. Furthermore, it is proved that this solution is the unique solution of the undertaken inverse problem. A numerical example is given to illustrate ill‐posedness of the inverse problem. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
19.
Yibing Lv Tiesong Hu Zhongping Wan 《Journal of Computational and Applied Mathematics》2008,220(1-2):175-180
In order to consider the inverse optimal value problem under more general conditions, we transform the inverse optimal value problem into a corresponding nonlinear bilevel programming problem equivalently. Using the Kuhn–Tucker optimality condition of the lower level problem, we transform the nonlinear bilevel programming into a normal nonlinear programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty. Then we give via an exact penalty method an existence theorem of solutions and propose an algorithm for the inverse optimal value problem, also analysis the convergence of the proposed algorithm. The numerical result shows that the algorithm can solve a wider class of inverse optimal value problem. 相似文献
20.
We consider an inverse problem for a one-dimensional integrodifferential hyperbolic system, which comes from a simplified model of thermoelasticity. This inverse problem aims to identify the displacement u, the temperature η and the memory kernel k simultaneously from the weighted measurement data of temperature. By using the fixed point theorem in suitable Sobolev spaces, the global in time existence and uniqueness results of this inverse problem are obtained. Moreover, we prove that the solution to this inverse problem depends continuously on the noisy data in suitable Sobolev spaces. For this nonlinear inverse problem, our theoretical results guarantee the solvability for the proposed physical model and the well-posedness for small measurement time τ, which is quite different from general inverse problems. 相似文献