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A novel regularization scheme for a backward problem in a sub-diffusion model
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DOI：10.1515/jiip-2024-0080.png)
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Abstract
En 中文
In this paper, an ill-posed problem of multi-term time-fraction diffusion equation with unknown initial values is considered. This is usually done by g := u( & sdot;, T) for some T > 0 to find u(x, t) for 0 <= t < T which is socalled backward problem. For convenience, we will label this problem as (Pt). Through analysis, we know that (Pt) is well posed for 0 < t < T, but ill-posed for t = 0 that is different from classical backward heat conduction problem. Therefore, a novel identification scheme of stable approximate solutions of ill-posed inverse problem (P0) is obtained by regularization family {Rt : 0 < t < T}, and the error estimates are analyzed under an a-priori and an a-posteriori regularization parameter choice rule and source conditions. Finally, some numerical examples are given to verify the effectiveness of the proposed method in one-and two-dimensional cases.
Keywords:
The multi-term time-fractional diffusion equation
backward problem
a novel regularization method
Journal
J
IF:
1
Papers:
48
Citations:
784