Identifying the Unknown Source in Linear Parabolic Equation by a Convoluting Equation Method

Zhenping Li, Xiangtuan Xiong and Qiang Cheng
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Zhenping Li: Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang 471023, China
Xiangtuan Xiong: Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Qiang Cheng: Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Mathematics, 2022, vol. 10, issue 13, 1-17

Abstract: This article is devoted to identifying a space-dependent source term in linear parabolic equations. Such a problem is ill posed, i.e., a small perturbation in the input data may cause a dramatically large error in the solution (if it exists). The conditional stability of the solution is analyzed. Based on a convoluting equation method, we can deal with the problem under the a priori parameter choice rule. Meanwhile, a modified version of Morozov’s discrepancy principle is provided to decide on an a posteriori regularization parameter choice strategy and a log-type error estimate is obtained. Two numerical results show that our proposed method works well.

Keywords: inverse source problem; ill posedness; regularization; parameter choice strategy; convergence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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