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An electrochemistry model with nonlinear diffusion: Steady-state solutions. (English) Zbl 0976.92035

From the introduction: We study a mathematical model of electrochemistry and we discuss the isentropic nonlinear diffusion model. The model will be formulated and then reduced to a boundary-value problem for a single non-local semilinear elliptic equation. Our objective includes the well-posedness of the mathematical model and numerical treatments to find the steady-state concentration distributions by using a globally convergent iteration scheme and Newton’s method. In addition, we illustrate that the nonlinear diffusion model is capable of providing an ideal complete separation of two species of opposite charge, which is not supported by the linear diffusion model. Our analysis and treatments can also be applied to the linear diffusion model and thus provide a uniform approach to both models.

MSC:

92E99 Chemistry
45K05 Integro-partial differential equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
65N99 Numerical methods for partial differential equations, boundary value problems
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