Recovering an unknown coefficient in an absorption model with diffusion

Денисов, А. М.; Lorenzi, Alessandra De

doi:10.1515/jiip.2007.033

Cited by 7 publications

(1 citation statement)

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“…A modern technique for obtaining sorption isotherms involves solving an inverse problem so that the simulated dynamic quantity coincides with the actual experimental results. During the last decades, certain inverse problems in estimating sorption isotherms and other parameters in some dynamic PDE models have been intensively studied, for example, [3,5,10,14,20,22,23,[25][26][27][29][30][31]. We also refer to [1,2,7,8,12,[15][16][17][18][19]28] for more related inverse problem studies.…”

Section: Introductionmentioning

confidence: 99%

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

Shcheglov¹,

Li²,

Wang³

et al. 2024

AAMM

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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.

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