JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (8): 35-42.doi: 10.6040/j.issn.1671-9352.0.2017.005

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Convergence analysis for inverse problems in a degenerate parabolic equation

ZHANG Tai-nian, LI Zhao-xing   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2017-01-11 Online:2017-08-20 Published:2017-08-03

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Abstract: This paper consider an inverse problem of reconstructing the principal coefficient in a second order degenerate parabolic equation of non-divergence form by using some additional observation data. It is transformed into an optimal control problem. The major problem is that the principal coefficient is unknown, but the degenerate degree of equation is determined, in general, by the principal coefficient. By introducing some weighted Sobolev spaces and some new source conditions, and adding a strong regularity condition to the admissible function set of the principal term, we prove the convergence of the optimal solution.

Key words: optimal control, Gâ, convergence, teaux derivative, inverse problem, degenerate parabolic equation

CLC Number: 

  • O175.26
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