Solution method for the inverse boundary-value problem for the wave equation

Existence and uniqueness issues are considered for the inverse boundary-value problem of determining the variable coefficient of the one-dimensional wave equation on a half-line. A Tikhonov-regularizing algorithm is constructed to find an approximate solution using input data that are specified with an error.Translated from Metody Matematicheskogo Modelirovaniya, Avtomatizatsiya Obrabotki Nablyudenii i Ikh Primeneniya, pp. 80–88, 1986.     

An inverse spectral problem for integro-differential Dirac operators with general convolution kernels

ABSTRACT

An integro-differential Dirac system with a convolution kernel consisting of four independent functions is considered. We prove that the kernel is uniquely determined by specifying the spectra of two boundary value problems with one common boundary condition. The proof is based on the reduction of this nonlinear inverse problem to solving some nonlinear integral equation, which we solve globally. On this basis we also obtain a constructive procedure for solving the inverse problem along with necessary and sufficient conditions for its solvability in an appropriate class of kernels.     

Solution of an inverse problem for estimation of ionospheric parameters

Translated from Matematicheskie Modeli i Optimizatsiya Vychislitel'nykh Algoritmov, pp. 75–81, 1994.     

Half-inverse problem for the Dirac operator

Given the spectrum of the Dirac operator, together with the potential on the half-interval and one boundary condition, this paper provides reconstruction of the potential on the whole interval, and proves the existence conditions of the solution.     

Two-dimensional inverse dynamic problem for the system of Maxwell equations

Osh and Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 3, pp. 7–20, May–June, 1992.     

Solution of Goursat problem for the Maxwell-Bloch system

A formal method of solving the initial—boundary-value problem in the quadrantx0,t0 for the Maxwell-Bloch system of equations is presented in terms of the inverse scattering problem.Institute of Mathematics, Urals Branch, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 1, pp. 29–37, January, 1994.     

Solution of the inverse scattering problem for the Landau-Lifshits equation by the Gel'fand-Levitan-Marchenko method

Moscow Institute of Steel and Alloys. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 23, No. 3, pp. 73–75, July–September, 1989.     

Solution of the inverse problem for an evolution equation in a Banach space

For the equationdy (t)/dt=Ay(t) + p, t [0, ), where A is a closed linear operator on a Banach space , p is an unknown parameter from , we consider the problem

Solution of inverse Lamb's problem with an unknown source

Translated from Chislennye Metody Resheniya Obratnykh Zadach Matematicheskoi Fiziki, pp. 5–9.     

On an inverse scattering problem for a class of Dirac operators with spectral parameter in the boundary condition

In this work, we consider the inverse scattering problem for a class of one dimensional Dirac operators on the semi-infinite interval with the boundary condition depending polynomially on a spectral parameter. The scattering data of the given problem is defined and its properties are examined. The main equation is derived, its solvability is proved and it is shown that the potential is uniquely recovered in terms of the scattering data. A generalization of the Marchenko method is given for a class of Dirac operator.