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Advances in Mathematical Physics
Volume 2018, Article ID 4628346, 19 pages
Research Article

The Inverse Problem of Identification of Hydrogen Permeability Model

Institute of Applied Mathematical Research of the Karelian Research Centre of the Russian Academy of Sciences, 11 Pushkinskaya St., Petrozavodsk 185910, Russia

Correspondence should be addressed to Yury V. Zaika; ur.ailerak.crk@akiaz

Received 7 December 2017; Accepted 2 May 2018; Published 7 June 2018

Academic Editor: Alexander Iomin

Copyright © 2018 Yury V. Zaika et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


One of the technological challenges for hydrogen materials science is the currently active search for structural materials with important applications (including the ITER project and gas-separation plants). One had to estimate the parameters of diffusion and sorption to numerically model the different scenarios and experimental conditions of the material usage (including extreme ones). The article presents boundary value problems of hydrogen permeability and thermal desorption with dynamical boundary conditions. A numerical method is developed for TDS spectrum simulation, where only integration of a nonlinear system of low order ordinary differential equations is required. The main final output of the article is a noise-resistant algorithm for solving the inverse problem of parametric identification for the aggregated experiment where desorption and diffusion are dynamically interrelated (without the artificial division of studies into the diffusion limited regime (DLR) and the surface limited regime (SLR)).