Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 382, Issue 1, Pages 474-486Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2011.04.070
Keywords
Inverse problem; Heat conduction equation; Binary functional; Uniqueness; Stability
Categories
Funding
- NNSF of China [11061018, 10972095]
- NSF of Gansu Province of China [0916RJZA046]
- Fundamental Research Funds for Universities in the Gansu Province of China [620004]
Ask authors/readers for more resources
The local well-posedness of the minimizer of an optimal control problem is studied in this paper. The optimization problem concerns an inverse problem of simultaneously reconstructing the initial temperature and heat radiative coefficient in a heat conduction equation. Being different from other ordinary optimization problems, the cost functional constructed in the paper is a binary functional which contains two independent variables and two independent regularization parameters. Particularly, since the status of the two unknown coefficients in the cost functional are different, the conjugate theory which is extensively used in single-parameter optimization problems cannot be applied for our problem. The necessary condition which must be satisfied by the minimizer is deduced. By assuming the terminal time T is relatively small, an L-2 estimate regarding the minimizer is obtained, from which the uniqueness and stability of the minimizer can be deduced immediately. (C) 2011 Elsevier Inc. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available