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

作　　者：Alexey Shcheglov Jingzhi Li Chao Wang Alexander Ilin Ye Zhang 

机构地区：[1]Faculty of Computational Mathematics and Cybernetics,Shenzhen MSU-BIT University,Shenzhen,Guangdong 518172,China [2]Faculty of Computational Mathematics and Cybernetics,Lomonosov Moscow State University,Moscow,Russia [3]Department of Mathematics&National Center for Applied Mathematics Shenzhen&SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong 518055,China [4]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China

出　　处：《Advances in Applied Mathematics and Mechanics》2024年第1期237-252,共16页应用数学与力学进展（英文）

基　　金：supported by the National Natural Science Foundation of China(No.12171036);Beijing Natural Science Foundation(No.Z210001);the NSF of China No.11971221,Guangdong NSF Major Fund No.2021ZDZX1001,the Shenzhen Sci-Tech Fund Nos.RCJC20200714114556020,JCYJ20200109115422828 and JCYJ20190809150413261,National Center for Applied Mathematics Shenzhen,and SUSTech International Center for Mathematics.

摘　　要：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.

关 键 词：Inverse problem quasi-linear dynamic model UNIQUENESS method of successive approximations stability 

分 类 号：O313[理学—一般力学与力学基础]