Recovery of non-smooth radiative coefficient from nonlocal observation by diffusion system

Recovery of non-smooth radiative coefficient from nonlocal observation by diffusion system AbstractThe heat conduction process in composite medium can be modeled by a parabolic equation with discontinuous radiative coefficient.To detect the composite medium characterized by such a non-smooth coefficient from measurable information about the heat distribution, we consider a nonlinear inverse problem for parabolic equation, with the average measurement of temperature field in some time interval as the inversion input.We firstly establish the uniqueness for this nonlinear inverse problem, based on the property of the direct problem and the known uniqueness result for linear inverse source problem.To solve the inverse problem from a nonlinear operator equation, the differentiability and the tangential condition of this nonlinear map is analyzed.An iterative process called two-point gradient method is proposed by minimizing data-fit term and the penalty term alternatively, with rigorous convergence analysis in terms of the tangential condition.Numerical simulations are presented to illustrate the effectiveness of the proposed method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inverse and III-posed Problems de Gruyter

Recovery of non-smooth radiative coefficient from nonlocal observation by diffusion system

Loading next page...
 
/lp/de-gruyter/recovery-of-non-smooth-radiative-coefficient-from-nonlocal-observation-KQhtHKLW2e
Publisher
de Gruyter
Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1569-3945
eISSN
1569-3945
DOI
10.1515/jiip-2019-0029
Publisher site
See Article on Publisher Site

Abstract

AbstractThe heat conduction process in composite medium can be modeled by a parabolic equation with discontinuous radiative coefficient.To detect the composite medium characterized by such a non-smooth coefficient from measurable information about the heat distribution, we consider a nonlinear inverse problem for parabolic equation, with the average measurement of temperature field in some time interval as the inversion input.We firstly establish the uniqueness for this nonlinear inverse problem, based on the property of the direct problem and the known uniqueness result for linear inverse source problem.To solve the inverse problem from a nonlinear operator equation, the differentiability and the tangential condition of this nonlinear map is analyzed.An iterative process called two-point gradient method is proposed by minimizing data-fit term and the penalty term alternatively, with rigorous convergence analysis in terms of the tangential condition.Numerical simulations are presented to illustrate the effectiveness of the proposed method.

Journal

Journal of Inverse and III-posed Problemsde Gruyter

Published: Jun 1, 2020

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