共查询到20条相似文献,搜索用时 292 毫秒
1.
Summary For the numerical solution of inverse Helmholtz problems the boundary value problem for a Helmholtz equation with spatially variable wave number has to be solved repeatedly. For large wave numbers this is a challenge. In the paper we reformulate the inverse problem as an initial value problem, and describe a marching scheme for the numerical computation that needs only n2 log n operations on an n × n grid. We derive stability and error estimates for the marching scheme. We show that the marching solution is close to the low-pass filtered true solution. We present numerical examples that demonstrate the efficacy of the marching scheme. 相似文献
2.
The dynamic inverse seismics problem is considered in a generalized setting. We investigate whether the wave propagation problem in a vertically nonhomogeneous medium is well-posed. We show that the regular part of the solution is an L
2 function and the inverse problem, i.e., the determination of the reflection coefficient, is thus reducible to minimizing the error functional. The gradient of the functional is obtained in explicit form from the conjugate problem, and approximate formulas for its evaluation are derived. A regularization algorithm for the solution of the inverse problem is considered; simulation results using various excitation sources are reported. 相似文献
3.
S. M. Koval'chuk 《Journal of Mathematical Sciences》1998,90(2):2042-2047
We consider the inverse problem of simultaneously determining two time-dependent thermophysical characteristics—the coefficient
of thermal conductivity and the heat capacity per unit volume—for a body having the shape of a layer situated between two
other layers with known thermophysical characteristics. The necessary measurements are carried out on their outside boundaries.
The problem is reduced to a system of nonlinear equations for which the existence of a solution is established by using Schauder's
fixed-point theorem. We find conditions that guarantee that the solution of the inverse problem is unique.
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 153–159. 相似文献
4.
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
5.
Nguyen Huy Tuan Nguyen Hoang Tuan Dumitru Baleanu Tran Ngoc Thach 《Mathematical Methods in the Applied Sciences》2020,43(3):1292-1312
In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L2 and Hτ norms is considered and illustrated by numerical example. 相似文献
6.
D. K. Durdiev 《Theoretical and Mathematical Physics》2008,156(2):1154-1158
We solve the problem of determining the hyperbolic equation coefficient depending on two variables. Some additional information
is given by the trace of the direct problem solution on the hyperplane x = 0. We estimate the stability of the solution of the inverse problem under study and prove the uniqueness theorem.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 220–225, August, 2008. 相似文献
7.
In this paper we consider the inverse problem of constructing an n × n real nonnegative matrix A from the prescribed partial eigendata. We first give the solvability conditions for the inverse problem without the nonnegative
constraint and then discuss the associated best approximation problem. To find a nonnegative solution, we reformulate the
inverse problem as a monotone complementarity problem and propose a nonsmooth Newton-type method for solving its equivalent
nonsmooth equation. Under some mild assumptions, the global and quadratic convergence of our method is established. We also
apply our method to the symmetric nonnegative inverse problem and to the cases of prescribed lower bounds and of prescribed
entries. Numerical tests demonstrate the efficiency of the proposed method and support our theoretical findings. 相似文献
8.
This paper considers the following inverse optimization problem: given a linear program, a desired optimal objective value, and a set of feasible cost vectors, determine a cost vector such that the corresponding optimal objective value of the linear program is closest to the desired value. The above problem, referred here as the inverse optimal value problem, is significantly different from standard inverse optimization problems that involve determining a cost vector for a linear program such that a pre-specified solution vector is optimal. In this paper, we show that the inverse optimal value problem is NP-hard in general. We identify conditions under which the problem reduces to a concave maximization or a concave minimization problem. We provide sufficient conditions under which the associated concave minimization problem and, correspondingly, the inverse optimal value problem is polynomially solvable. For the case when the set of feasible cost vectors is polyhedral, we describe an algorithm for the inverse optimal value problem based on solving linear and bilinear programming problems. Some preliminary computational experience is reported.Mathematics Subject Classification (1999):49N45, 90C05, 90C25, 90C26, 90C31, 90C60Acknowledgement This research has been supported in part by the National Science Foundation under CAREER Award DMII-0133943. The authors thank two anonymous reviewers for valuable comments. 相似文献
9.
Mourad Bellassoued 《Applicable analysis》2013,92(10):983-1014
One of the basic inverse problems in an anisotropic media is the determination of coefficients in a bounded domain with a single measurement. We consider the problem of finding the coefficient of the second derivatives in a second-order hyperbolic equation with variable coefficients. Under a weak regularity assumption and a geometrical condition on the metric, we prove the uniqueness in a multidimensional hyperbolic inverse problem with a single measurement. Moreover we show that our uniqueness results yield the Lipschitz stability estimate in L 2 space for solution to the inverse problem under consideration. 相似文献
10.
Mokhtar Kirane Salman A. Malik Mohammed A. Al‐Gwaiz 《Mathematical Methods in the Applied Sciences》2013,36(9):1056-1069
We consider the inverse source problem for a time fractional diffusion equation. The unknown source term is independent of the time variable, and the problem is considered in two dimensions. A biorthogonal system of functions consisting of two Riesz bases of the space L2[(0,1) × (0,1)], obtained from eigenfunctions and associated functions of the spectral problem and its adjoint problem, is used to represent the solution of the inverse problem. Using the properties of the biorthogonal system of functions, we show the existence and uniqueness of the solution of the inverse problem and its continuous dependence on the data. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
11.
A. Boutet de Monvel 《Journal of Difference Equations and Applications》2013,19(8):711-727
We construct the transformation operator for the scattering problem with a periodic background under the assumption that the coefficients of the perturbation have a first finite moment. By means of the Marchenko approach [Marchenko, V. (1986) Sturm–Liouville Operators and Applications. Birkhäuser, Basel, Switzerland] we derive an estimate on the kernel of this transformation operator that allow us to study the inverse problem solution in the prescribed class of perturbations. 相似文献
12.
Roger Knobel Joyce R. McLaughlin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1994,45(5):794-826
In this paper we describe a method for constructing approximate solutions of a two-dimensional inverse eigenvalue problem. Here we consider the problem of recovering a functionq(x, y) from the eigenvalues of — +q(x, y) on a rectangle with Dirichlet boundary conditions. The potentialq(x, y) is assumed to be symmetric with respect to the midlines of the rectangle. Our method is a generalization of an algorithm Hald presented for the construction of symmetric potentials in the one-dimensional inverse Sturm-Liouville problem. Using a projection method, the inverse spectral problem is reduced to an inverse eigenvalue problem for a matrix. We show that if the given eigenvalues are small perturbations of simple eigenvalues ofq=0, then the matrix problem has a solution. This solution is used to construct a functionq which has the same lowest eigenvalues as the unknownq, and several numerical examples are given to illustrate the methods. 相似文献
13.
B. V. Gera 《Journal of Mathematical Sciences》1997,86(2):2578-2584
We propose a statement and computational scheme for the inverse problem of recovering the temperature field and the moisture
distribution in a body with incompletely known initial conditions. We give additional relations on the integral values of
the unknown functions and introduce a test for the choice of a unique solution of the problem from the set of admissible temperature
and moisture functions. We state conditions for independence of the additional data and obtain systems of equations and conditions
that close the initial indeterminate problem. We study in detail the example of heat-moisture conduction in a layer.
Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 66–73. 相似文献
14.
V. L. Kamynin 《Differential Equations》2011,47(1):91-101
We study existence and uniqueness of the solution for the inverse problem of determination of the unknown coefficient ϱ(t) multiplying u
t
in a nondivergence parabolic equation. As additional information, the integral of the solution over the domain of space variables
with some given weight function is specified. The coefficients of the equation depend both on time and on the space variables. 相似文献
15.
Pham Loi Vu 《Acta Appl Math》2010,109(3):789-787
We derive the continual system of nonlinear interaction waves from the compatibility of the transport equation on the whole
line and the equation governing the time-evolution of the eigenfunctions of the transport operator. The transport equation
represents the continual generalization from the n-component system of first-order ordinary differential equations. The continual system describes a nonlinear interaction of
waves. We prove that the continual system can be integrated by the inverse scattering method. The method is based on applying
the results of the inverse scattering problem for the transport equation to finding the solution of the Cauchy initial-value
problem for the continual system. Indeed, the transition operator for the scattering problem admits right and left Volterra
factorizations. The intermediate operator for this problem determines the one-to-one correspondence between the preimages
of a solution of the transport equation. This operator is related to the transition operator and admits not only right and
left Volterra factorizations but also the analytic factorization. By virtue of this fact the potential in the transport equation
is uniquely reconstructed in terms of the solutions of the fundamental equations in inverse problem. 相似文献
16.
We consider a problem for a quasilinear hyperbolic equation with a nonlocal condition that contains a retarded argument. By reducing this problem to a nonlinear integrofunctional equation, we prove the existence and uniqueness theorem for its solution. We pose an inverse problem of finding a solution-dependent coefficient of the equation on the basis of additional information on the solution; the information is given at a fixed point in space and is a function of time. We prove the uniqueness theorem for the solution of the inverse problem. The proof is based on the derivation and analysis of an integro-functional equation for the difference of two solutions of the inverse problem. 相似文献
17.
V. L. Kamynin 《Differential Equations》2012,48(2):214-223
We study the existence and uniqueness of the solution of the inverse problem of finding an unknown coefficient b(x) multiplying the lower derivative in the nondivergence parabolic equation on the plane. The integral of the solution with
respect to time with some given weight function is given as additional information. The coefficients of the equation depend
on the time variable as well as the space variable. 相似文献
18.
We recently proposed in [Cheng, XL et al. A novel coupled complex boundary method for inverse source problems Inverse Problem 2014 30 055002] a coupled complex boundary method (CCBM) for inverse source problems. In this paper, we apply the CCBM to inverse conductivity problems (ICPs) with one measurement. In the ICP, the diffusion coefficient q is to be determined from both Dirichlet and Neumann boundary data. With the CCBM, q is sought such that the imaginary part of the solution of a forward Robin boundary value problem vanishes in the problem domain. This brings in advantages on robustness and computation in reconstruction. Based on the complex forward problem, the Tikhonov regularization is used for a stable reconstruction. Some theoretical analysis is given on the optimization models. Several numerical examples are provided to show the feasibility and usefulness of the CCBM for the ICP. It is illustrated that as long as all the subdomains share some portion of the boundary, our CCBM-based Tikhonov regularization method can reconstruct the diffusion parameters stably and effectively. 相似文献
19.
V. L. Kamynin 《Differential Equations》2018,54(5):633-647
We obtain theorems on the proximity as t → +∞ between the solution of the inverse problem for a second-order degenerate parabolic equation with one spatial variable and the solution of the inverse problem for a second-order degenerate ordinary differential equation under an additional integral observation condition. The conditions imposed on the input data admit oscillations of the functions on the right-hand side in the parabolic equation under study. 相似文献
20.
We study the inverse problem of determining the multidimensional kernel of the integral term in a parabolic equation of second order. As additional information, the solution of the direct problem is given on the hyperplane x n = 0. We prove a local existence and uniqueness theorem for the inverse problem. 相似文献