On local solvability of inverse dissipative scattering problems
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A. V. Baev
Abstract
- Much work has been done on inverse scattering problems for one-dimensional acoustic media. Unfortunately, the linear method of the Gel’fand - Levitan integral equations is developed only for inversion from reflection data in case of negligible dissipative effects. On the contrary, measurement data, in geophysical prospecting particularly, are often influenced by these effects. The main result of this paper is a necessary and sufficient condition of solvability of the inverse dissipative scattering problem with data given on a finite time interval. We also consider a bilinear procedure for recovering the dissipation coefficient from the reflection data. The approach is based on a step-by-step split method for numerical solution of a system of the Gel’fand - Levitan integral equations under nonlocal boundary conditions. Besides, we develop a method of inversion of difference schemes for solving the inverse dissipative scattering problems.
© 2013 by Walter de Gruyter GmbH & Co.
Articles in the same Issue
- Contents
- Carleman’s formulas for the Laplace and Poisson equations with operator coefficients
- On local solvability of inverse dissipative scattering problems
- Sourcewise representation of solutions to nonlinear operator equations in a Banach space and convergence rate estimates for a regularized Newton’s method
- Iterative methods for an inverse heat conduction problem
- Identification of a special class of memory kernels in one-dimensional heat flow
- Nonlinear inverse problems for elliptic equations
- Inverse problem for interior spectral data of the Sturm – Liouville operator
Articles in the same Issue
- Contents
- Carleman’s formulas for the Laplace and Poisson equations with operator coefficients
- On local solvability of inverse dissipative scattering problems
- Sourcewise representation of solutions to nonlinear operator equations in a Banach space and convergence rate estimates for a regularized Newton’s method
- Iterative methods for an inverse heat conduction problem
- Identification of a special class of memory kernels in one-dimensional heat flow
- Nonlinear inverse problems for elliptic equations
- Inverse problem for interior spectral data of the Sturm – Liouville operator
