Abstract
Abstract
This paper is devoted to two backward problems in a time-fractional diffusion-wave equation, with the aid of extra measurement data at a final time. Since these two problems are ill-posed, a quasi-reversibility method is obtained by employing eigenfunction expansion, and the existence, uniqueness and regularity of the regularized solutions are also proven. We can get order-optimal error estimates from the a-priori parameter choice rule. Finally, several numerical examples of both one- and two-dimension show that the proposed regularization method is effective and stable.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Gansu Province
Scientific research project of Higher School in Gansu Province
Project of NWNU-LKQN
Subject
Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics
Cited by
1 articles.
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