Convergence of finite-difference scheme inversion in problems of determining the coefficients in hyperbolic equations

Convergence of finite-difference scheme inversion in problems of determining the coefficients in... -- As is known, a broad class of inverse problems for hyperbolic equations and systems reduces to the Volterra operator equations of the first or second kind with Volterra and boundedly Lipschitzcontinuous kernels [15-17]. In this work the above properties are shown to ensure the well-posedness of inverse problems locally and in the neighborhood of the exact solution as a whole. The procedure developed allows us to estimate the rate of convergence in the finite-difference scheme inversion method in solving the inverse problems for hyperbolic equations and systems. 1. POSING THE PROBLEM AND EXAMPLES The problems of determining the coefficients in hyperbolic equations and systems using some additional information on their solution are of great practical importance. The unknown coefficients, as a rule, are such important characteristics of the media being studied as Lamo parameters and density in case of an inverse problem in the theory of elasticity, the tensors of dielectric permittivity, magnetic permeability and conductivity in case of an inverse problem in electrodynamics; the velocity of wave propagation in a medium and density in case of an inverse problem in acoustics and so on. The inverse problems for hyperbolic equations belong to ill-posed problems of mathematical http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inverse and Ill-Posed Problems de Gruyter

Convergence of finite-difference scheme inversion in problems of determining the coefficients in hyperbolic equations

Loading next page...
 
/lp/de-gruyter/convergence-of-finite-difference-scheme-inversion-in-problems-of-X8PYz9dRh2
Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0928-0219
eISSN
1569-3945
DOI
10.1515/jiip.1993.1.1.33
Publisher site
See Article on Publisher Site

Abstract

-- As is known, a broad class of inverse problems for hyperbolic equations and systems reduces to the Volterra operator equations of the first or second kind with Volterra and boundedly Lipschitzcontinuous kernels [15-17]. In this work the above properties are shown to ensure the well-posedness of inverse problems locally and in the neighborhood of the exact solution as a whole. The procedure developed allows us to estimate the rate of convergence in the finite-difference scheme inversion method in solving the inverse problems for hyperbolic equations and systems. 1. POSING THE PROBLEM AND EXAMPLES The problems of determining the coefficients in hyperbolic equations and systems using some additional information on their solution are of great practical importance. The unknown coefficients, as a rule, are such important characteristics of the media being studied as Lamo parameters and density in case of an inverse problem in the theory of elasticity, the tensors of dielectric permittivity, magnetic permeability and conductivity in case of an inverse problem in electrodynamics; the velocity of wave propagation in a medium and density in case of an inverse problem in acoustics and so on. The inverse problems for hyperbolic equations belong to ill-posed problems of mathematical

Journal

Journal of Inverse and Ill-Posed Problemsde Gruyter

Published: Jan 1, 1993

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off