Two-dimensional parabolic inverse source problem with final overdetermination in reproducing kernel space
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A new method of the reproducing kernel Hilbert space is applied to a two-dimensional parabolic inverse source problem with the final overdetermination. The exact and approximate solutions are both obtained in a reproducing kernel space. The approximate solution and its partial derivatives are proved to converge to the exact solution and its partial derivatives, respectively. A technique is proposed to improve some existing methods. Numerical results show that the method is of high precision, and confirm the robustness of our method for reconstructing source parameter.
KeywordsInverse source problem Final overdetermination Parabolic equation Reproducing kernel
2000 MR Subject Classification35K55 47B32
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