International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 23, Pages 1447-1463
Nonlinear dynamical boundary-value problem of hydrogen thermal
Institute of Applied Mathematical Research, Karelian Research Centre, Petrozavodsk, Russia
Received 25 March 2002
Copyright © 2003 Yu. V. Zaika and I. A. Chernov. 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.
The nonlinear boundary-value problem for the diffusion equation,
which models gas interaction with solids, is considered. The
model includes diffusion and the sorption/desorption processes on
the surface, which leads to dynamical nonlinear boundary
conditions. The boundary-value problem is reduced to an
integro-differential equation of a special kind; existence and
uniqueness of the classical (differentiable) solution theorems
are proved. The results of numerical experiments are presented.