Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm (Advances in Applied Mathematics and Mechanics, 2023)
This study addresses the parameter identification problem in a system oftime-dependent quasi-linear partial differential equations (PDEs). Using the integralequation 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 algorithmare proven under both a priori and a posteriori stopping rules. A numerical example isgiven to show the efficiency and robustness of the proposed new approach.