JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (10): 61-71.doi: 10.6040/j.issn.1671-9352.0.2018.093

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Time dependent parabolic inverse source problem based on variational theory

ZHEN Wei-wei, ZENG Jian, REN Jian-long   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2018-03-09 Online:2018-10-20 Published:2018-10-09

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Abstract: The problem of source term reconstruction for a class of parabolic equation with variable coefficients is studied, and the source term here is only time dependent. Different from the previous work, the additional condition in this paper is about the integration of the spatial variable, this type of additional conditions can help to eliminate the errors caused by random selection. At the same time, it will lead to many analysis methods unavailable. Based on the variational theory, firstly, the variational formula is given and the uniqueness of the solution is proved by the variational formula; Secondly, the time discrete model is given, and based on the variational form of linear discretization, a series of priori estimates are derived and the existence of weak solutions is proved.

Key words: uniqueness, variational theory, existence of weak solution, inverse source problem

CLC Number: 

  • O175.26
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