Regularization of backward time-fractional parabolic equations by Sobolev-type equations

Dinh Nho Hào, Nguyen Van Duc, Nguyen Van Thang, Nguyen Trung Thành

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


The problem of determining the initial condition from noisy final observations in time-fractional parabolic equations is considered. This problem is well known to be ill-posed, and it is regularized by backward Sobolev-type equations. Error estimates of Hölder type are obtained with a priori and a posteriori regularization parameter choice rules. The proposed regularization method results in a stable noniterative numerical scheme. The theoretical error estimates are confirmed by numerical tests for one- and two-dimensional equations.

Original languageEnglish (US)
Pages (from-to)659-676
Number of pages18
JournalJournal of Inverse and Ill-Posed Problems
Issue number5
StatePublished - Oct 1 2020

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


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