JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (8): 56-66.doi: 10.6040/j.issn.1671-9352.0.2023.232

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Identification of nonlinear heat transfer law of heat conduction equation

Le DU(),Liu YANG*(),Tao ZHANG   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2023-05-24 Online:2024-08-20 Published:2024-07-31
  • Contact: Liu YANG E-mail:l_du1678@163.com;l_yang218@163.com

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Abstract:

The identification of temperature-dependent heat transfer coefficients in heat conduction equations by boundary control is considered. Based on the optimal control theory, the general heat conduction equation parameter inversion problem is transformed into a variational problem, and then the existence and necessary conditions of the minimum value are discussed. Finally, by using the energy norm estimation method, the uniqueness and stability of the minimum value are proved under the assumption that the terminal time is small.

Key words: heat conduction equation, inverse problem, nonlinear heat transfer law, nonlinear boundary, optimal control

CLC Number: 

  • O175.26
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