Identification of unknown diffusion and convection coefficients in ion transport problems from flux data: an analytical approach |
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Authors: | Alemdar Hasanov |
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Institution: | 1.Department of Mathematics and Computer Sciences,Izmir University,Uckuyular, Izmir,Turkey |
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Abstract: | This article presents an analytical approach for identification problems related to ion transport problems. In the first part
of the study, relationship between the flux jL : = (D(x)ux(0, t)x=0{\varphi_L := (D(x)u_x(0, t)_{x=0}} and the current response I(t){{\mathcal I}(t)} is analyzed for various models. It is shown that in pure diffusive linear model case the flux is proportional to the classical
Cottrelian IC(t){{\mathcal I}_C(t)}. Similar relationship is derived in the case of nonlinear model including diffusion and migration. These results suggest
acceptability of the flux data as a measured output data in ion transport problems, instead of nonlocal additional condition
in the form an integral of concentration function. In pure diffusive and diffusive-convective linear models cases, explicit
analytical formulas between inputs (diffusion or/and convection coefficients) and output (measured flux data) are derived.
The proposed analytical approach permits one to determine the unknown diffusion coefficient from a single flux data given
at a fixed time t
1 > 0, and unknown convection coefficient from a single flux data given at a fixed time t
2 > t
1 > 0. Linearized model of the nonlinear ion transport problem with variable diffusion and convection coefficients is analyzed.
It is shown that the measured output (flux) data can not be given arbitrarily. |
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Keywords: | |
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