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Iterative method for solving an inverse coefficient problem for a hyperbolic equation

Iterative method for solving an inverse coefficient problem for a hyperbolic equation 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Iterative method for solving an inverse coefficient problem for a hyperbolic equation

Differential Equations , Volume 53 (7) – Aug 23, 2017

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References (18)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266117070084
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Differential EquationsSpringer Journals

Published: Aug 23, 2017

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