Two-Dimensional Parabolic Inverse Source Problem with Final Overdetermination in Reproducing Kernel Space

A new method of the reproducing kernel Hilbert space is applied to a twodimensional 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...

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Bibliographic Details
Published in:Chinese annals of mathematics. Serie B 2014-05, Vol.35 (3), p.469-482
Main Authors: Wang, Wenyan, Yamamoto, Masahiro, Han, Bo
Format: Article
Language:English
Subjects:
Applications of Mathematics
Final
Mathematics
Mathematics and Statistics
二维
再生核Hilbert空间
再生核空间
反源问题
抛物型
计算结果
近似解
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Summary:A new method of the reproducing kernel Hilbert space is applied to a twodimensional 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.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-014-0831-2