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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 ϕ L :=(D(x)u x (0,t) x=0 and the current response (t) is analyzed for various models. It is shown that in pure diffusive linear model case the flux is proportional to the classical Cottrelian 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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