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Volume 16, Issue 1
Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm

Alexey Shcheglov, Jingzhi Li, Chao Wang, Alexander Ilin & Ye Zhang

DOI: 10.4208/aamm.OA-2023-0020

Adv. Appl. Math. Mech., 16 (2024), pp. 237-252.

Published online: 2023-12

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  • 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.

  • Keywords

Inverse problem, quasi-linear dynamic model, uniqueness, method of successive approximations, stability.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-16-237, author = {Shcheglov , AlexeyLi , JingzhiWang , ChaoIlin , Alexander and Zhang , Ye}, title = {Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2023}, volume = {16}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0020}, url = {http://global-sci.org/intro/article_detail/aamm/22297.html} }
TY - JOUR T1 - Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm AU - Shcheglov , Alexey AU - Li , Jingzhi AU - Wang , Chao AU - Ilin , Alexander AU - Zhang , Ye JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 237 EP - 252 PY - 2023 DA - 2023/12 SN - 16 DO - http://doi.org/10.4208/aamm.OA-2023-0020 UR - https://global-sci.org/intro/article_detail/aamm/22297.html KW - Inverse problem, quasi-linear dynamic model, uniqueness, method of successive approximations, stability. AB -

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.

Shcheglov , AlexeyLi , JingzhiWang , ChaoIlin , Alexander and Zhang , Ye. (2023). Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm. Advances in Applied Mathematics and Mechanics. 16 (1). 237-252. doi:10.4208/aamm.OA-2023-0020
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