Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 362, Issue 1, Pages 210-223Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2009.08.042
Keywords
Inverse problem; Heat conduction equation; Radiative coefficient; Optimal control; Existence; Uniqueness; Stability
Categories
Funding
- NNSF of China [10572051]
- NSF of Gansu province of China [3ZS051-A25-030]
- Lanzhou Jiaotong University [409043]
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This paper studies an evolutional type inverse problem of identifying the radiative coefficient of heat conduction equation when the over-specified data is given. Problems of this type have important applications in several fields of applied science. Being different from other ordinary inverse coefficient problems, the unknown coefficient in this paper depends on both the space variable x and the time t. Based on the optimal control framework, the inverse problem is transformed into an optimization problem and a new cost functional is constructed in the paper. The existence, uniqueness and stability of the minimizer of the cost functional are proved, and the necessary conditions which must be satisfied by the minimizer are also given. The results obtained in the paper are interesting and useful, and can be extended to more general parabolic equations. (C) 2009 Elsevier Inc. All rights reserved.
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