<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper deals with the problem of determining an unknown source and an unknown initial condition in a abstract final value parabolic problem. This problem is ill-posed in the sense that the solutions do not depend continuously on the data. To solve the considered problem a modified Tikhonov regularization method is proposed. Using this method regularized solutions are constructed and under boundary conditions assumptions, convergence estimates between the exact solutions and their regularized approximations are obtained. Moreover numerical results are presented to illustrate the accuracy and efficiency of the proposed method.</p></abstract>

This paper deals with the problem of determining an unknown source and an unknown initial condition in a abstract final value parabolic problem. This problem is ill-posed in the sense that the solutions do not depend continuously on the data. To solve the considered problem a modified Tikhonov regularization method is proposed. Using this method regularized solutions are constructed and under boundary conditions assumptions, convergence estimates between the exact solutions and their regularized approximations are obtained. Moreover numerical results are presented to illustrate the accuracy and efficiency of the proposed method.

A modified Tikhonov regularization method for a class of inverse parabolic problems

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper deals with the problem of determining an unknown source and an unknown initial condition in a abstract final value parabolic problem. This problem...

A modified Tikhonov regularization method for a class of inverse parabolic problems

Published Online: Apr 09, 2020

Page range: 181 - 204

Received: Mar 01, 2019

Accepted: May 01, 2019

DOI: https://doi.org/10.2478/auom-2020-0013

Keywords
Parabolic problem, ill-posed problem, inverse problem, modified Tikhonov regularization, error estimate

© 2020 Nabil Saouli et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A modified Tikhonov regularization method for a class of inverse parabolic problems

Published Online: Apr 09, 2020

Page range: 181 - 204

Received: Mar 01, 2019

Accepted: May 01, 2019

DOI: https://doi.org/10.2478/auom-2020-0013

KeywordsParabolic problem, ill-posed problem, inverse problem, modified Tikhonov regularization, error estimate

© 2020 Nabil Saouli et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Parabolic problem, ill-posed problem, inverse problem, modified Tikhonov regularization, error estimate