<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

Publié en ligne: 09 avr. 2020

Pages: 181 - 204

Reçu: 01 mars 2019

Accepté: 01 mai 2019

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

Mots clés
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

Publié en ligne: 09 avr. 2020

Pages: 181 - 204

Reçu: 01 mars 2019

Accepté: 01 mai 2019

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

Mots clésParabolic 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.

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