Simultaneous inversion of coefficient and source term of a one-dimensional reaction-diffusion equation

被引：0
|
作者：
Zhao Z.-X. [1 ]
Guo B.-Z. [2 ]
Han Z.-J. [3 ]
机构：
[1] School of Mathematical Science, Tianjin Normal University, Tianjin
[2] School of Mathematics and Physics, North China Electric Power University, Beijing
[3] School of Mathematics, Tianjin University, Tianjin
来源：
Kongzhi Lilun Yu Yingyong/Control Theory and Applications | 2022年 / 39卷 / 09期
关键词：
inverse problems; matrix pencil method; optimal perturbation regularization; parameter identification; reaction-diffusion equation; switch on/off boundary control;
D O I：
10.7641/CTA.2022.10992
中图分类号：
学科分类号：
摘要：
Reaction-diffusion equations are widely used in the modeling of many physical, chemical and biological processes. This paper investigates simultaneous inversion of the reaction coefficient and source term for a one-dimensional reaction-diffusion equation based on boundary control and boundary observation. To begin with, by virtue of the uniqueness of the Dirichlet series representation and inverse spectral theory, it is shown that the reaction coefficient and source term can be uniquely determined from the boundary observation by designing a switch on/off boundary control. Next, a stable numerical algorithm is proposed for the simultaneous reconstruction of the reaction coefficient and source term by combining the matrix pencil method and optimal perturbation regularization technique. Finally, the effectiveness of the identification algorithm is verified by a numerical example. © 2022 South China University of Technology. All rights reserved.
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页码：1601 / 1608
页数：7
相关论文
共 22 条
  • [1] CANTRELL R S, COSNER C., Spatial Ecology Via Reaction-Diffusion Equations, (2003)
  • [2] LI Gongsheng, TAN Yongji, WANG Xiaoqin, Inverse problem method on determining magnitude of groundwater pollution sources, Mathematica Applicata, 18, 1, pp. 92-98, (2005)
  • [3] AVDONIN S, SEIDMAN T I., Identification of q(x) in ut = ∆u − qu from boundary observations, SIAM Journal on Control and Optimization, 33, 4, pp. 1247-1255, (1995)
  • [4] BOUMENIR A, TUAN V K., Inverse problems for multidimensional heat equations by measurements at a single point on the boundary, Numerical Functional Analysis and Optimization, 30, 11, pp. 1215-1230, (2009)
  • [5] JOHANSSON B T, LESNIC D., A variational method for identifying a spacewise-dependent heat source, IMA Journal of Applied Mathematics, 72, 6, pp. 748-760, (2007)
  • [6] YANG L, DEHGHAN M, YU J N, Et al., Inverse problem of time-dependent heat sources numerical reconstruction, Mathematics and Computers in Simulation, 81, 8, pp. 1656-1672, (2011)
  • [7] HUSSEIN M S, LESNIC D, JOHANSSON B T, Et al., Identification of a multi-dimensional space-dependent heat source from boundary data, Applied Mathematical Modelling, 54, pp. 202-220, (2018)
  • [8] RUNDELL W, ZHANG Z D., On the identification of source term in the heat equation from sparse data, SIAM Journal on Mathematical Analysis, 52, 2, pp. 1526-1548, (2020)
  • [9] HASANOV A., An inverse source problem with single Dirichlet type measured output data for a linear parabolic equation, Applied Mathematics Letters, 24, 7, pp. 1269-1273, (2011)
  • [10] AL-MUSALLAM F, BOUMENIR A., The reconstruction of a source and a potential from boundary measurements, Journal of Mathematical Analysis and Applications, 435, 1, pp. 800-808, (2016)
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