Name
Title | ||
|---|---|---|
Identification of the time-dependent source term in a multi-term time-fractional diffusion equation |
Abstract | ||
|---|---|---|
The multi-term time-fractional diffusion equation is a useful tool in the modeling of complex systems. This paper aims to identifying a time-dependent source term in a multi-term time-fractional diffusion equation from the boundary Cauchy data. The regularity of the weak solution for the direct problem with homogeneous Neumann boundary condition is proved. We provide the uniqueness and a stability estimate for the inverse time-dependent source problem. On the other hand, the inverse time-dependent source term is formulated into a variational problem by the Tikhonov regularization, with the help of sensitivity problem and adjoint problem we use a conjugate gradient method to find the approximate time-dependent source term. Numerical experiments for five examples in one-dimensional and two-dimensional cases show that our proposed method is effective and stable. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s11075-019-00654-5 | Numerical Algorithms |
Keywords | DocType | Volume |
Inverse source problem, Multi-term time-fractional diffusion equation, Conjugate gradient method | Journal | 82 |
Issue | ISSN | Citations |
4 | 1017-1398 | 0 |
PageRank | References | Authors |
0.34 | 4 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Y. S. Li | 1 | 0 | 0.68 |
| Liangliang Sun | 2 | 6 | 3.66 |
| Z. Q. Zhang | 3 | 5 | 1.34 |
| T. Wei | 4 | 87 | 18.96 |