Abstract
A time-dependent Poisson–Nernst–Planck system of nonlinear partial differential equations of a mixed parabolic-elliptic type is considered. The generalized model is supplemented by a positivity and volume constraints, by dual entropy variables, and by nonlinear boundary conditions. The existence theorem supported by a priori estimates, the Lyapunov stability of the solution, and its uniqueness in a special case are proved.
Mathematics Subject Classification (2010). Primary 35D05; Secondary 35M10, 37B25, 82C24.
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Kovtunenko, V.A., Zubkova, A.V. (2017). Solvability and Lyapunov Stability of a Two-component System of Generalized Poisson–Nernst–Planck Equations. In: Maz'ya, V., Natroshvili, D., Shargorodsky, E., Wendland, W. (eds) Recent Trends in Operator Theory and Partial Differential Equations. Operator Theory: Advances and Applications, vol 258. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-47079-5_9
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DOI: https://doi.org/10.1007/978-3-319-47079-5_9
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-47077-1
Online ISBN: 978-3-319-47079-5
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