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

Autor:	Zhenping Li, Xiangtuan Xiong, Qiang Cheng
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	inverse source problem ill posedness regularization parameter choice strategy convergence analysis Mathematics QA1-939
Zdroj:	Mathematics, Vol 10, Iss 13, p 2191 (2022)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math10132191
Popis:	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.
Databáze:	Directory of Open Access Journals
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