FAN, Bin; AZAIEZ, Mejdi; XU, Chuanju

doi:10.3934/dcdss.2020409

Institut de Mécanique et d'Ingénierie [I2M]

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Article de revue

Ce document a été publié dans

Discrete and Continuous Dynamical Systems - Series S. 2021-01-01, vol. 14, n° 8, p. 2893

Résumé en anglais

In this paper, we investigate numerical methods for a backward problem of the time-fractional wave equation in bounded domains. We propose two fractional filter regularization methods, which can be regarded as an extension of the classical Landweber iteration for the time-fractional wave backward problem. The idea is first to transform the ill-posed backward problem into a weighted normal operator equation, then construct the regularization methods for the operator equation by introducing suitable fractional filters. Both a priori and a posteriori regularization parameter choice rules are investigated, together with an estimate for the smallest regularization parameter according to a discrepancy principle. Furthermore, an error analysis is carried out to derive the convergence rates of the regularized solutions generated by the proposed methods. The theoretical estimate shows that the proposed fractional regularizations efficiently overcome the well-known over-smoothing drawback caused by the classical regularizations. Some numerical examples are provided to confirm the theoretical results. In particular, our numerical tests demonstrate that the fractional regularization is actually more efficient than the classical methods for problems having low regularity.< Réduire

Mots clés en anglais

Backward problem

Time-fractional wave equation

Fractional filter regularization

Convergence

URI

https://oskar-bordeaux.fr/handle/20.500.12278/110215

DOI

http://dx.doi.org/10.3934/dcdss.2020409

Project ANR

Méthode des champs : algorithmes et simulations de phénomènes complexes - ANR-16-CE40-0026
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003

Unités de recherche

Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295

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An extension of the landweber regularization for a backward time fractional wave problem