JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (2): 88-98.doi: 10.6040/j.issn.1671-9352.0.2024.220

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Identification of radiation coefficients for nonlinear parabolic equations with variable coefficients

LONG Chang, YANG Liu*   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2026-02-13

Abstract: In this paper, we study a class of inverse problems that use additional conditions to reconstruct the radiation coefficients of nonlinear parabolic equations with variable coefficients, where the variable coefficient of the equation depends on the gradient of the solution. Firstly, the uniqueness and stability of the corresponding solution to definite solutions problem are proved by energy estimation. Secondly, based on the optimal control theory, the original problem is transformed into an optimization problem by using Tikhonov regularization method. Finally, the existence, uniqueness and stability of the minimum element are proved by using the necessary conditions satisfied by the minimum.

Key words: inverse problem, nonlinear parabolic equations, optimal control

CLC Number: 

  • O175
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