共查询到20条相似文献,搜索用时 15 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.
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
3.
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
4.
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
5.
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
6.
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
7.
The inverse problem for the FitzHugh-Nagumo and Aliev-Panfilov models describing wave propagation in excitable media is considered. The problem lies in determining a localized initial condition from measurements on the external boundary of a plane region. A numerical method for solving the inverse problem is proposed, and the results from a numerical solution of the inverse problem for regions similar to different sections of a heart are presented. 相似文献
8.
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
9.
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
10.
The Note is concerned with an inverse source problem for the Helmholtz equation, which determines the source from measurements of the radiated field away at multiple frequencies. Our main result is a novel stability estimate for the inverse source problem. Our result indicates that the ill-posedness of the inverse problem decreases as the frequency increases. Computationally, a continuation method is introduced to solve the inverse problem by capturing both the macro and the small scales of the source function. A numerical example is presented to demonstrate the efficiency of the method. 相似文献
11.
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
12.
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
13.
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
14.
TONG Chongliang~ CHENG Jin~ 《中国科学A辑(英文版)》2005,48(1):40-56
The inverse problem of determining two convection coefficients of an ellipticpartial differential equation by Dirichlet to Neumann map is discussed.It is well knownthat this is a severely ill-posed problem with high nonlinearity.By the inverse scatteringtechnique for first order elliptic system in the plane and the theory of generalized analyticfunctions,we give a constructive method for this inverse problem. 相似文献
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17.
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
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.
Heike Faßbender 《Numerische Mathematik》1997,77(3):323-345
Summary. This paper explores the relationship between certain inverse unitary eigenvalue problems and orthogonal functions. In particular,
the inverse eigenvalue problems for unitary Hessenberg matrices and for Schur parameter pencils are considered. The Szeg?
recursion is known to be identical to the Arnoldi process and can be seen as an algorithm for solving an inverse unitary Hessenberg
eigenvalue problem. Reformulation of this inverse unitary Hessenberg eigenvalue problem yields an inverse eigenvalue problem
for Schur parameter pencils. It is shown that solving this inverse eigenvalue problem is equivalent to computing Laurent polynomials
orthogonal on the unit circle. Efficient and reliable algorithms for solving the inverse unitary eigenvalue problems are given
which require only O() arithmetic operations as compared with O() operations needed for algorithms that ignore the structure of the problem.
Received April 3, 1995 / Revised version received August 29, 1996 相似文献
20.
D. V. Churbanov A. Yu. Shcheglov 《Computational Mathematics and Mathematical Physics》2013,53(2):215-220
For a partial differential equation simulating population dynamics, the inverse problem of determining its nonlinear right-hand side from an additional boundary condition is studied. This inverse problem is reduced to a functional equation, for which the existence and uniqueness of a solution is proven. An iterative method for solving this inverse problem is proposed. The accuracy of the method is estimated, and restrictions on the number of steps are obtained. 相似文献