Boundary Control and Observation to Inverse Coefficient Problem for Heat Equation With Unknown Source and Initial Value

This article investigates an inverse problem of determining the spatially variable diffusion coefficient of a one-dimensional heat equation with an unknown spatial varying source term and initial value. The big challenge of the problem comes from the multiple unknowns and very limited available data...

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Vydané v:IEEE transactions on automatic control Ročník 66; číslo 12; s. 6003 - 6010
Hlavní autori: Zhao, Zhi-Xue, Guo, Bao-Zhu, Han, Zhong-Jie
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.12.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Algorithms
Boundary control
Diffusion
Diffusion coefficient
Heat equation
inverse coefficient problem (ICP)
Inverse problems
Mathematical analysis
Mathematical model
matrix pencil method (MPM)
Numerical analysis
optimal perturbation regularization algorithm
Perturbation
Perturbation methods
Regularization
switch <sc xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">on/off control
Temperature measurement
Thermodynamics
ISSN:0018-9286, 1558-2523
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Popis
Shrnutí:This article investigates an inverse problem of determining the spatially variable diffusion coefficient of a one-dimensional heat equation with an unknown spatial varying source term and initial value. The big challenge of the problem comes from the multiple unknowns and very limited available data that are only boundary control and boundary observation at one end, in addition to the ill-posed nature of the inverse problem. We first design a switch on/off boundary control and show that the diffusion coefficient can be uniquely determined by the boundary observation. Next, a stable numerical algorithm for reconstruction of the diffusion coefficient is proposed by means of the matrix pencil method and optimal perturbation regularization technique. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed identification algorithm.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3058905