Academy of Mathematics and Systems Science, CAS Colloquia & Seminars | Speaker: | 王泽文 教授,东华理工大学 | Inviter: | | Title: | Exponential Tikhonov regularization method for solving an inverse source problem of time fractional diffusion equations | Time & Venue: | 2021.11.05 10:00-11:00 腾讯会议号:536 387 062 会议链接 https://meeting.tencent.com/dm/muYRYc1VPxm2 | Abstract: | In this talk, we mainly study an inverse source problem of time fractional diffusion equation in a bounded domain with an over-specified terminal condition at a fixed time. A novel regularization method, which we call the exponential Tikhonov regularization method with a parameter , is proposed to solve the inverse source problem, and the corresponding convergence analyses are given under a-priori and a-posteriori regularization parameter choice rules. When is less than or equal to zero, the optimal convergence rate can be achieved and it is independent of the value of . However, when is great than zero, the optimal convergence rate depends on the value of which is related to the regularity of the unknown source. Finally, numerical experiments are conducted for showing the effectiveness of the proposed exponential regularization method. | | | |