JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (4): 127-134.doi: 10.6040/j.issn.1671-9352.0.2015.268

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An inverse problem of identifying the coefficient in a Kolmogorov type equation

CAI Chao   

  1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2015-06-08 Online:2016-04-20 Published:2016-04-08

Abstract: This work investigates an inverse problem of reconstructing the convection coefficient in a Kolmogorov equation from the final measurement data, which has important application in many fields of applied science. Compared with ordinary inverse problems, the unknown coefficient in this work depends on both the space variable x and the time variable t. On the basis of the optimal control framework, the identification problem is transformed into an optimization problem and the existence of the minimizer for the cost functional is established. Then necessary condition of the minimizer is obtained. After the necessary condition of the minimizer satisfied, the stability and uniqueness of the minimizer are deduced.

Key words: optimal control, existence, uniqueness, inverse problem, stability, Kolmogorov equation

CLC Number: 

  • O175.26
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