Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm

Shcheglov, Alexey1,2; Li, Jingzhi3,4,5; Wang, Chao1; Ilin, Alexander2; Zhang, Ye6

2023-04-01

10.4208/aamm.OA-2023-0020

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS   Impact Factor & Quartile

2070-0733

2075-1354

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 iter-ative 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.

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

SCI

English

Others

National Natural Science Foundation of China[12171036] ; Beijing Natural Science Foundation[Z210001] ; NSF of China[11971221] ; Guangdong NSF Major Fund[2021ZDZX1001] ; Shenzhen Sci-Tech Fund["RCJC20200714114556020","JCYJ20200109115422828","JCYJ20190809150413261"] ; Guangdong Youth Innovation Talents Project[2022KQNCX108] ; GuangDong Basic and Applied Basic Research Foundation[2022A1515110362]

Mathematics ; Mechanics

Mathematics, Applied ; Mechanics

WOS:001084235800001

GLOBAL SCIENCE PRESS

Web of Science

1.Shenzhen MSU BIT Univ, Fac Computat Math & Cybernet, Shenzhen 518172, Guangdong, Peoples R China
2.Lomonosov Moscow State Univ, Fac Computat Math & Cybernet, Moscow, Russia
3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
4.Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen, Shenzhen 518055, Guangdong, Peoples R China
5.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen 518055, Guangdong, Peoples R China
6.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

Shcheglov, Alexey,Li, Jingzhi,Wang, Chao,et al. Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm[J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS,2023.

Shcheglov, Alexey,Li, Jingzhi,Wang, Chao,Ilin, Alexander,&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.

Shcheglov, Alexey,et al."Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm".ADVANCES IN APPLIED MATHEMATICS AND MECHANICS (2023).