Fang, Weifu; Ito, Kazufumi An electrochemistry model with nonlinear diffusion: Steady-state solutions. (English) Zbl 0976.92035 IMA J. Appl. Math. 66, No. 2, 195-213 (2001). 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. Cited in 2 Documents 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 Keywords:existence and uniqueness of solutions; global convergence; integro-differential equations; electrochemistry; nonlinear diffusion model; semilinear elliptic equation PDFBibTeX XMLCite \textit{W. Fang} and \textit{K. Ito}, IMA J. Appl. Math. 66, No. 2, 195--213 (2001; Zbl 0976.92035) Full Text: DOI