Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm
Year: 2024
Author: Alexey Shcheglov, Jingzhi Li, Chao Wang, Alexander Ilin, Ye Zhang
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 1 : pp. 237–252
Abstract
This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations (PDEs). Using the integral equation method, we prove the uniqueness of the inverse problem in nonlinear PDEs. Moreover, using the method of successive approximations, we develop a novel iterative algorithm to estimate sorption isotherms. The stability results of the algorithm are proven under both a priori and a posteriori stopping rules. A numerical example is given to show the efficiency and robustness of the proposed new approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0020
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 1 : pp. 237–252
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Inverse problem quasi-linear dynamic model uniqueness method of successive approximations stability.