共查询到20条相似文献,搜索用时 62 毫秒
1.
A. M. Denisov 《Differential Equations》2017,53(7):916-922
For a hyperbolic equation, we consider an inverse coefficient problem in which the unknown coefficient occurs in both the equation and the initial condition. The solution values on a given curve serve as additional information for determining the unknown coefficient. We suggest an iterative method for solving the inverse problem based on reduction to a nonlinear operator equation for the unknown coefficient and prove the uniform convergence of the iterations to a function that is a solution of the inverse problem. 相似文献
2.
A. M. Denisov 《Differential Equations》2009,45(11):1577-1587
We consider two inverse coefficient problems for a quasilinear hyperbolic equation, where the additional information used
for finding the coefficients is the values of the solution on some curve. (This corresponds to measurements performed at a
moving observation point.) The unknown coefficient depends on the space variable in the first inverse problem and on the solution
of the equation in the second inverse problem. We prove theorems of uniqueness of solution to the inverse problems. 相似文献
3.
A. M. Denisov 《Differential Equations》2016,52(9):1142-1149
We consider an inverse coefficient problem for a linear system of partial differential equations. The values of one solution component on a given curve are used as additional information for determining the unknown coefficient. The proof of the uniqueness of the solution of the inverse problem is based on the analysis of the unique solvability of a homogeneous integral equation of the first kind. The existence of a solution of the inverse problem is proved by reduction to a system of nonlinear integral equations. 相似文献
4.
Galyna A. Snitko 《Journal of Mathematical Sciences》2014,200(3):374-388
The present paper deals with the inverse problem of determination of the coefficient of the first derivative of the unknown function with respect to a spatial variable for a one-dimensional parabolic equation in the domain whose boundary is determined by two unknown functions. The conditions of local existence and uniqueness of a solution to the inverse problem are established. 相似文献
5.
This paper deals with the problem of determining of an unknown coefficient in an inverse boundary value problem. Using a nonconstant overspecified data, it has been shown that the solution to this inverse problem exists and is unique. 相似文献
6.
V. L. Kamynin 《Differential Equations》2014,50(6):792-804
We obtain existence and uniqueness theorems for the solution of the inverse problem of simultaneously determining the right-hand side and the coefficient of a lower-order derivative in a parabolic equation under an integral observation condition. We give explicit estimates for the maximum absolute value of the unknown right-hand side and the unknown coefficient of the equation with constants expressed via the input data of the problem. We present a nontrivial example of an inverse problem to which our theorems apply. 相似文献
7.
A. V. Baev 《Differential Equations》2017,53(8):981-988
We consider a nonclassical ordinary differential equation containing not only an unknown function but also an unknown coefficient depending on the unknown function. We show that if the desired solution is assumed to have bounded variation and be a.e. constant on the interval where the equation is considered, then the problem of finding the solution and the unknown coefficient does not have a unique solution in terms of the classical derivative. We prove that if the derivative is understood as a distribution, than this problem has a unique solution. These results are used to show that the acoustic impedance and the damping factor in the inverse scattering problem in a layered dissipative medium can be determined simultaneously. 相似文献
8.
O. V. Drozhzhina 《Computational Mathematics and Modeling》2003,14(4):350-359
The article considers the inverse problem of determining the nonlinear right-hand side of a quasi-linear parabolic equation and proves a uniqueness theorem. A method is proposed for numerical solution of the inverse problem based on parametric representation of the sought coefficient. The inverse problem thus reduces to finding the error-minimizing vector of unknown coefficients of the parametric representation of the sought function. 相似文献
9.
A. Sh. Lyubanova 《Differential Equations》2014,50(4):502-512
We consider inverse problems of finding an unknown coefficient in the leading term of a linear pseudoparabolic equation of filtration type on the basis of integral data over the entire boundary or its part under the assumption that the unknown coefficient depends on time. We derive conditions for the time-global solvability and uniqueness of the solution of the inverse problem. 相似文献
10.
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
11.
V. L. Kamynin 《Mathematical Notes》2013,94(1-2):205-213
Existence and uniqueness theorems for the solution to the inverse problem of determining the lower-order coefficient in multidimensional parabolic equations with integral observation are obtained. An estimate of the maximum of the modulus of the unknown coefficient with a constant explicitly expressed via the input data of the problem is given. 相似文献
12.
We consider an inverse problem for a one-dimensional parabolic equation with unknown time-dependent major coefficient in a
domain whose unknown boundary weakly degenerates at the initial time moment. The conditions for existence and uniqueness of
the classical solution of the problem are established. 相似文献
13.
A. M. Denisov E. V. Zakharov A. V. Kalinin V. V. Kalinin 《Differential Equations》2009,45(7):1034-1043
We consider numerical methods for solving inverse problems that arise in heart electrophysiology. The first inverse problem
is the Cauchy problem for the Laplace equation. Its solution algorithm is based on the Tikhonov regularization method and
the method of boundary integral equations. The second inverse problem is the problem of finding the discontinuity surface
of the coefficient of conductivity of a medium on the basis of the potential and its normal derivative given on the exterior
surface. For its numerical solution, we suggest a method based on the method of boundary integral equations and the assumption
on a special representation of the unknown surface. 相似文献
14.
This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained. 相似文献
15.
M. I. Ivanchov 《Ukrainian Mathematical Journal》2000,52(3):379-387
We establish conditions for the unique existence of a solution of the inverse problem of simultaneous determination of two
unknown coefficients in a parabolic equation. One of these coefficients is the leading coefficient that depends on time, and
the other coefficient depends on a space variable. 相似文献
16.
利用压缩映像原理讨论了一类半线性波方程确定未知系数的反问题,文中给出了该问题解的存在性、唯一性和稳定性。 相似文献
17.
We propose a new numerical method for estimating the piecewise constant Robin coefficient in two-dimensional elliptic equation from boundary measurements. The Robin inverse problem is recast into a minimization of an output least-square formulation. A technique based on determining the discontinuous points of the unknown coefficient is suggested, and we investigate the differentiability of the solution and the objective functional with respect to the discontinuous points. Then we apply the Gauss-Newton method for reconstructing the shape of the unknown Robin coefficient. Numerical examples illustrate its efficiency and stability. 相似文献
18.
In this article we consider the inverse problem of identifying a time dependent unknown coefficient in a parabolic problem subject to initial and non-local boundary conditions along with an overspecified condition defined at a specific point in the spatial domain. Due to the non-local boundary condition, the system of linear equations resulting from the backward Euler approximation have a coefficient matrix that is a quasi-tridiagonal matrix. We consider an efficient method for solving the linear system and the predictor–corrector method for calculating the solution and updating the estimate of the unknown coefficient. Two model problems are solved to demonstrate the performance of the methods. 相似文献
19.
ABSTRACT Considered in this paper is an inverse Robin problem governed by a steady-state diffusion equation. By the Robin inverse problem, one wants to recover the unknown Robin coefficient on an inaccessible boundary from Cauchy data measured on the accessible boundary. In this paper, instead of reconstructing the Robin coefficient directly, we compute first the Cauchy data on the inaccessible boundary which is a linear inverse problem, and then compute the Robin coefficient through Newton's law. For the Cauchy problem, a parameter-dependent coupled complex boundary method (CCBM) is applied. The CCBM has its own merits, and this is particularly true when it is applied to the Cauchy problem. With the introduction of a positive parameter, we can prove the regularized solution is uniformly bounded with respect to the regularization parameter which is a very good property because the solution can now be reconstructed for a rather small value of the regularization parameter. For the problem of computing the Robin coefficient from the recovered Cauchy data, a least square output Tikhonov regularization method is applied to Newton's law to obtain a stable approximate Robin coefficient. Numerical results are given to show the feasibility and effectiveness of the proposed method. 相似文献
20.
Tao Lin 《Applied mathematics and computation》1998,90(2-3):253-284
A C0 finite element method is presented for an inverse problem in which the coefficient in the differential operator is to be determined from the measurement of the solution of a boundary value problem. The unknown in the inverse problem is approximated by a minimizer of a cost function that includes both the output error and equation error. Error estimates in a weighted H−1 norm and L2 are given. Numerical examples are presented to show features of the method. 相似文献