科研之友
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摘要
We consider the problem of identifying an unknown source which depends on the spatial variable, in a heat equation. This is an ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. To obtain a stable numerical solution, we propose an interesting regularization method based on the idea of quasi-reversibility method. The error estimate between the exact solution and its regularized approximation is given. We also discuss the numerical implementation and give several examples to verify the effectiveness of the proposed method.
