4.1 Article

An inverse problem of identifying the source coefficient in a degenerate heat equation

Journal

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
Volume 23, Issue 3, Pages 498-517

Publisher

TAYLOR & FRANCIS LTD
DOI: 10.1080/17415977.2014.922079

Keywords

49J20; 35R30; stability; uniqueness; degenerate parabolic equation; existence; optimal control; inverse problem; numerical results

Funding

  1. National Natural Science Foundation of China [11061018, 11261029]
  2. Youth Foundation of Lanzhou Jiaotong University [2011028]
  3. Long Yuan Young Creative Talents Support Program [252003]
  4. NSF of Gansu Province of China [1212RJZA043]
  5. Innovative Research Group Foundation of Gansu Province of China [1308RJIA006]
  6. Research Fund for the Doctoral Program of Higher Education of China [20126204110001]

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The aim of this work is to reconstruct a spacewise dependent heat source in a degenerate heat equation using the final measurement temperature. Based on the optimal control framework, the inverse problem is transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional are established, and the global uniqueness and stability of the minimizer are also obtained from the necessary condition. Finally, a numerical algorithm on the basis of the conjugate gradient method is designed to treat the inverse problem and some numerical experiments are also performed. The numerical results show that the algorithm designed in the paper is quite efficient and stable, and the unknown heat source is recovered very well.

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