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arXiv · 2004.07349

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

Dinh Nho Hao·Nguyen Van Duc·Nguyen Van Thang·Nguyen Trung Thanh
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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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Dinh Nho Hao, Nguyen Van Duc, Nguyen Van Thang, Nguyen Trung Thanh. 2020-04-15. Regularization of backward time-fractional parabolic equations by Sobolev-type equations. https://arxiv.org/abs/2004.07349

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