Identification of a Time Dependent Source Function in a Parabolic Inverse Problem Via Finite Element Approach

J. Damirchi (), R. Pourgholi (), T. R. Shamami (), H. Zeidabadi () and A. Janmohammadi ()
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J. Damirchi: Semnan University
R. Pourgholi: Damghan University
T. R. Shamami: Semnan University
H. Zeidabadi: Sabzevar University of New Technology
A. Janmohammadi: Semnan University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1587-1602

Abstract: Abstract In the present paper, we study one-dimensional inverse source problem of identifying a time-dependent source function from the over-specification condition. The unknown source term is recovered by solving an operator integral equation of the first kind. Due to the ill-posedness of this operator integral equation, the Tikhonov regularization approach of the 1st order is applied in order to acquire a stable approximation. The stable solution is defined by minimization of the Tikhonov functional. The value of the regularization parameter in this method is obtained as a function of error in input data. The finite element method is applied for numerical simulation based on obtained results. The illustrative example is presented to show the accuracy and applicability of the proposed method.

Keywords: Inverse source problem; ill-posed operator equation; Tikhonov regularization method; finite element method; regularization parameter; 47A52; 35K05; 35R30; 65M70 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0483-8

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