Regularization of backward time-fractional parabolic equations by Sobolev equations methods
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It is well-known that backward parabolic equations in which the initial condition is to be determined from a measurement at a later time instant is ill-posed. In this paper, a regularization method for backward time-fractional parabolic equations by the Sobolev equations method is investigated. 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 with numerical tests for one and two dimensional equations.
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