Regularization of backward time-fractional parabolic equations by Sobolev-type equations
Numerical Analysis
2020-09-11 v2 Numerical Analysis
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
Keywords
Cite
@article{arxiv.2004.07349,
title = {Regularization of backward time-fractional parabolic equations by Sobolev-type equations},
author = {Dinh Nho Hao and Nguyen Van Duc and Nguyen Van Thang and Nguyen Trung Thanh},
journal= {arXiv preprint arXiv:2004.07349},
year = {2020}
}