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 - <p style="text-align: justify;">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.</p>