共查询到20条相似文献,搜索用时 31 毫秒
1.
V. A. Yurko 《Differential Equations》2016,52(3):335-345
We study boundary value problems on a hedgehog graph for second-order ordinary differential equations with a nonlinear dependence on the spectral parameter. We establish properties of spectral characteristics and consider the inverse spectral problem of reconstructing the coefficients of a differential pencil on the basis of spectral data. For this inverse problem, we prove a uniqueness theorem and obtain a procedure for constructing its solution. 相似文献
2.
V. A. Yurko 《Differential Equations》2011,47(1):50-59
We study the inverse problem of spectral analysis for Sturm-Liouville operators on A-graphs. We obtain a constructive procedure
for solving the inverse problem of reconstruction of coefficients of differential operators from spectra and prove the uniqueness
of the solution. 相似文献
3.
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
4.
We study non-self-adjoint second-order differential operators with a constant delay. We establish properties of the spectral characteristics and investigate the inverse problem of recovering operators from their spectra. The uniqueness theorem is proved for this inverse problem. 相似文献
5.
Chuan-Fu Yang 《Israel Journal of Mathematics》2014,204(1):431-446
An inverse nodal problem is studied for a differential pencil with non-separated boundary conditions. We prove that a dense subset of nodal points uniquely determines the boundary data and potential functions. We also provide a constructive procedure for the solution of the inverse nodal problem. 相似文献
6.
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
7.
V. A. Yurko 《Differential Equations》2008,44(12):1721-1729
We study boundary value problems on noncompact cycle-free graphs (i.e., trees) for second-order ordinary differential equations with a nonlinear dependence on the spectral parameter. We establish properties of the spectrum and analyze the inverse problem of reconstructing the coefficients of a differential equation on the basis of the so-called Weyl functions. For this inverse problem, we prove a uniqueness theorem and obtain a procedure for constructing the solution by the method of spectral mapping. 相似文献
8.
We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their spectra. We establish the uniqueness and develop a constructive algorithm for solution of the inverse problem. 相似文献
9.
《Mathematical Methods in the Applied Sciences》2018,41(4):1697-1702
A partial inverse problem for an integro‐differential Sturm‐Liouville operator on a star‐shaped graph is studied. We suppose that the convolution kernels are known on all the edges of the graph except one and recover the kernel on the remaining edge from a part of the spectrum. We prove the uniqueness theorem for this problem and develop a constructive algorithm for its solution, based on the reduction of the inverse problem on the graph to the inverse problem on the interval by using the Riesz basis property of the special system of functions. 相似文献
10.
V. A. Yurko 《Mathematical Notes》2011,89(3-4):438-449
We study the inverse spectral problem for Sturm-Liouville differential operators on hedgehog-type graphs with a cycle and with standard matching conditions at interior vertices. We prove a uniqueness theorem and obtain a constructive solution for this class of inverse problems. 相似文献
11.
We investigate a problem for the Dirac differential operators in the case where an eigenparameter not only appears in the
differential equation but is also linearly contained in a boundary condition. We prove uniqueness theorems for the inverse
spectral problem with known collection of eigenvalues and normalizing constants or two spectra. 相似文献
12.
The inverse problem of synthesizing parameters of differential systems having a finite number of arbitrary order singularities and turning points is investigated. We establish properties of the spectral characteristics, prove a uniqueness theorem and provide a prodcedure for constructing the solution of the inverse problem. 相似文献
13.
A. B. Evseev 《Computational Mathematics and Modeling》2003,14(3):334-344
We consider the quasi-linear problem of nonequilibrium sorption dynamics with external-diffusion kinetics and a boundary condition that contains the time derivative of a solution component. A numerical method is proposed for describing the inverse problem to recover the nonlinear parameter of the system of differential equations—the inverse of the sorption isotherm. Convergence of the difference scheme for the direct problem is proved. Numerical solutions of both the direct and the inverse problem are obtained for various parameter values. 相似文献
14.
V. Yurko 《Journal of Differential Equations》2008,244(2):431-443
We study boundary value problems on compact graphs without circles (i.e. on trees) for second-order ordinary differential equations with nonlinear dependence on the spectral parameter. We establish properties of the spectral characteristics and investigate the inverse spectral problem of recovering the coefficients of the differential equation from the so-called Weyl vector which is a generalization of the Weyl function (m-function) for the classical Sturm-Liouville operator. For this inverse problem we prove the uniqueness theorem and obtain a procedure for constructing the solution by the method of spectral mappings. 相似文献
15.
Vyacheslav Yurko 《Central European Journal of Mathematics》2014,12(3):483-499
We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness. 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.
Vjacheslav Yurko 《Mathematische Nachrichten》2000,211(1):177-183
We study the inverse problem of recovering differential operators of the Orr‐Sommerfeld type from the Weyl matrix. Properties of the Weyl matrix are investigated, and an uniqueness theorem for the solution of the inverse problem is proved. 相似文献
18.
We obtain conditions for the solvability of the inverse problem of the variational calculus for differential equations of second order with deviating argument of special form as well as the formula for the functional of the inverse problem defined by the integral that differs from the standard one by that the required function has a retarded argument. 相似文献
19.
V. A. Yurko 《Journal of Mathematical Sciences》2008,150(6):2620-2627
The inverse spectral problem of recovering pencils of second-order differential operators on the half-line with turning points
is studied. We give a formulation of the inverse problem, establish properties of the spectral characteristics, and prove
the uniqueness theorem for the solution of the inverse problem.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 5, pp. 237–246, 2006. 相似文献
20.
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