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

作者：Deng Zui Cha^*; Qian Kun; Rao Xiao Bo; Yang Liu; Luo Guan Wei

来源：Inverse Problems in Science and Engineering, 2015, 23(3): 498-517.

DOI：10.1080/17415977.2014.922079

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

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.

• 出版日期2015-4-3
• 单位兰州交通大学