New approach to identify the initial condition in degenerate hyperbolic equation

This paper deals with the determination of an initial condition in degenerate hyperbolic equation from final observations. With the aim of reducing the execution time, this inverse problem is solved using an approach based on double regularization: a Tikhonov's regularization and regularization...

Full description

Saved in:
Bibliographic Details
Published inInverse problems in science and engineering Vol. 27; no. 4; pp. 484 - 512
Main Authors Atifi, K., Essoufi, EL-H., Khouiti, B.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 03.04.2019
Subjects
adjoint method
Data assimilation
degenerate equations
inverse problem
optimization
regularization
wave equation
Online AccessGet full text

Cover

More Information
Summary:This paper deals with the determination of an initial condition in degenerate hyperbolic equation from final observations. With the aim of reducing the execution time, this inverse problem is solved using an approach based on double regularization: a Tikhonov's regularization and regularization in equation by viscose-elasticity. So, we obtain a sequence of weak solutions of degenerate linear viscose-elastic problems. Firstly, we prove the existence and uniqueness of each term of this sequence. Secondly, we prove the convergence of this sequence to the weak solution of the initial problem. Also we present some numerical experiments to show the performance of this approach.
ISSN:1741-5977
1741-5985
DOI:10.1080/17415977.2018.1471075