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Chinese Annals of Mathematics, Series B

, Volume 35, Issue 3, pp 469–482 | Cite as

Two-dimensional parabolic inverse source problem with final overdetermination in reproducing kernel space

  • Wenyan WangEmail author
  • Masahiro Yamamoto
  • Bo Han
Article

Abstract

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.

Keywords

Inverse source problem Final overdetermination Parabolic equation Reproducing kernel 

2000 MR Subject Classification

35K55 47B32 

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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinChina
  2. 2.Department of MathematicsNortheast Forestry UniversityHarbinChina
  3. 3.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan
  4. 4.Department of MathematicsHarbin Institute of TechnologyHarbinChina

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