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

2020/04/15 by Hao, Dinh Nho, Van Duc, Nguyen, Van Thang, Nguyen +1
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2004.07349

Abstract

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 Holder 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

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