A mollification regularization method for unknown source in time-fractional diffusion equation. (English) Zbl 1304.35755
Summary: In the present paper, we consider an inverse source problem for a fractional diffusion equation. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. We propose a mollification regularization method to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, a new a posteriori parameter choice rule is also proposed and a good error estimate is also obtained. Numerical examples are presented to illustrate the validity and effectiveness of this method.
MSC:
| 35R11 | Fractional partial differential equations |
| 35R25 | Ill-posed problems for PDEs |
| 47A52 | Linear operators and ill-posed problems, regularization |
| 65F22 | Ill-posedness and regularization problems in numerical linear algebra |
| 65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |
| 65J22 | Numerical solution to inverse problems in abstract spaces |
Keywords:
time-fractional diffusion equation; time-dependent heat source; mollification regularization method; a posteriori parameter choice; error estimateReferences:
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