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Identification of unknown diffusion and convection coefficients in ion transport problems from flux data: An analytical approach. (English) Zbl 05796512
Summary: 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 ${\varphi }_{L}:=\left(D\left(x\right){u}_{x}{\left(0,t\right)}_{x=0}$ and the current response $ℐ\left(t\right)$ is analyzed for various models. It is shown that in pure diffusive linear model case the flux is proportional to the classical Cottrelian ${ℐ}_{C}\left(t\right)$. 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.
##### MSC:
 92E Chemistry
##### References:
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