A mollification regularization method for identifying the time-dependent heat source problem. (English) Zbl 1380.65230
Summary: We study in this paper the problem of determining time-dependent source functions in a parabolic equation with data given at some fixed locations in the domain. To solve this ill-posed inverse problem, we develop a mollification regularization method with a Gaussian kernel. We derive an a priori error estimate between the exact solution and its regularized approximation. Moreover, we propose an a posteriori parameter choice strategy for the selection of the regularization strength and derive an error estimate associated with the strategy. Numerical results are presented to illustrate the accuracy and efficiency of our method.
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 35R25 | Ill-posed problems for PDEs |
| 35R30 | Inverse problems for PDEs |
| 47A52 | Linear operators and ill-posed problems, regularization |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Keywords:
a posteriori parameter choice; error estimate; identifying time-dependent source; ill-posedness; inverse source problem; mollification methods; parabolic equationReferences:
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